Every hero, especially cores, have a set of core items that have to be built on them most of the time (nothing is a fixed rule when it comes to items) in order to get them going: that includes boots, items like Battlefury on Antimage or Phantom Assassin, Blink on characters that have great difficulties in landing their abilities without it (Axe, Shaker etc. Others might have it as a situational choice). Past those, you have items you need in order to become effective, avoid the enemy team from making you ineffective, or consolidate your advantage, and aside from a few builds/heroes, they are mostly all situational: for example you ARE going to get a Daedalus on Kunkka at some point, any other choice would be less profitable, so it's not situational, but for example, a Heart of Tarrasque might be a better choice than a second Daedalus in certain situations.

This guide doesn't cover EVERY item of the game: it only covers situational options. For core items and boots you should check out an item build for your character of choice.

To experienced players: for the most part, this guide assumes experienced players already have sufficient knowledge to choose items for the right situations. The author isn't a pro player by any means, so it's possible that experienced players will find some of the indications questionable: in that case, they're welcome to comment about it. Keep in mind that the examples given are catered to less experienced players, as experts are likely to figure out good applications for certain items by themselves.
Please keep the comments informative so that missing informations can be added to the guide!

• Hand of Midas: you get it on heroes that need lots of pricey items and/or levels to be effective. By buying it you are sacrificing your effectiveness in the short run because you just spent 2050g on something that ultimately doesn't improve you directly in any way, so get it on the above mentioned type of heroes if you trust your team and composition can carry on without your help until you are ready to fight. Generally, only late carries buy it since it's not very advantageous on others.
  
• Soul Ring: obviously an early game choice. Needed on heroes that lack the mana to spam but do need to do so in order to control or at least survive the lane. Ideally you're sacrificing some gold to buy it so that you can get more by lasthitting more safely or even getting kills in lane. Apart from some heroes that almost always pick it up, you should ignore it if you or your carry can lasthit safely already or you have enough mana to keep your opponents in check. Typical heroes might be Sven, Dark Seer, Omniknight, Earthshaker...
  
• Medallion of Courage: good for physical, single-target oriented heroes and Roshan soloers like PA or Ursa, but also good on armour melting supports like Vengeful or Dazzle; I also like to pick it up on Bounty Hunter if I have to rapidly focus down some particular hero.
  
• Drum of Endurance: generally good on heroes that rely on their team and autoattack after having used their abilities, which includes initiators like Tusk but also carries like Juggernaut and Ember, since it supports their ability to fight even before having completed their build. It's good for teamfights and it's good for pushing, plus it's usually sold when the game advances so there's no need to be shy on the charges.
  
• Forcestaff: this is usually core on supports and INT heroes that don't have mobility skills but it can be a good situational option for others as well, for example as a tool to escape melee chasers like Ursa and Lifestealer, who have slows but no real way of stopping you: one of these on a fragile hero will make a difference between life and death. Also it's great even for offensive potential on heroes that rely a lot on positioning, like Dark Seer or Elder Titan.
  
• Battle Fury: heroes that pick it up have it as core. I can't think of any situational pickup of it. Generally it's picked up because it's great for melee carries that have difficulties farming: mana and HP regen, raw damage and cleave make it great for pushing waves and farming jungle even before lifesteal.
  
• Orb of Venom: it's worth picking it up early on roamers, gankers and other heroes that rely on early kills that don't have many ways of keeping the enemy from escaping to his tower early in the game. Examples are Ursa or Slark, and Venomancer loves to pick it up to add yet another poison effect to his stuff, making his early harrassing a beast.
  
• Enchanted Mango: this item is a good starting or early game item for heroes that have high mana costs and low mana pools such as strength heroes that rely on their abilities to be effective: Bristleback, Centaur Warrunner, Sven and the like. It's also very good on many heroes that choose to pick the offlane like Clockwerk or Ogre Magi since the extra regen helps against the harrass and the mana burst can help them use their abilities to get the space to farm before they get a Bottle or Soul Ring, at which point the level advantage and the mana from those items will allow them to get the upper hand even when outnumbered.

• Vladimir's Offering: it gives a lot of benefits, but the most notable is a melee lifesteal aura that's not a unique attack modifier and thus stacks with other lifesteals; if you desperately need both lifesteal and another UAM you can get them both using this (if you're melee; I can't imagine any ranged hero picking this up frankly). Most often it's a pick up for fighting supports (which are most often melee/STR) or heroes using summons or minions like Broodmother. I also love to pick this up on Beastmaster.
  
• Veil of Discord: pretty straightforward really: good on heroes that rely on spells for damage and on supports that can afford it to help their magic using allies.
  
• Eul's Scepter of Divinity: great for setting up comboes such as Lina's or Invoker's, and to grant an easier escape on heroes that rely on cooldowns for staying safe, such as Puck. It's also good on Death Prophet because her ult keeps up its effect even if she's disabled. Also, it has good offensive potential if you need to keep an enemy from using his spells or from escaping (it blocks Blink Dagger when they get back to the ground if used on enemies), unless of course they would benefit from the extra time. An Eul on an ulting Witch Doctor, Sven or Broodmother or a timely Eul on a Tidehunter that just blinked and is about to Ravage will make a good difference in the fight even if it will make those enemies temporarily invulnerable.
  
• Rod of Atos: great on INT bursters who would love their enemies being too slow to escape (like Skywrath, Dark Seer, Outworld Devourer or Leshrac), and also provides good HPs. Also a good counter to melee chasers: it can turn the tides against them very easily if you burst them down from just out of their reach.
  
• Orchid Malevolence: good on INT carries, especially if they rely on autoattack to some extent (such as Outworld Devourer), plus it's great against heroes that are very dangerous if left free to cast abilities or against heroes that can easily escape ganks: Orchid an Antimage or a Queen of Pain when ganking them and they'll be easy to focus down before they can flee. Also great on heroes that rely on being undisturbed when blitzing a single target, like Broodmother, Clinkz or Bounty Hunter.
  
• Aghanim's Scepter: obviously depends on the hero, but generally it's a good choice if you're going to rely a lot of what it improves: if you're building a late autoattack build on Luna or Beastmaster you might as well save this slot for other items. Generally if there's a choice between an Aghs build and a non-Aghs build, the Aghs one is oriented more towards the mid to late game than to the extra late game (Juggernaut is an exception with its atkspd build since it relies on ulti to make use of his autoattack safely). It's kinda core on heroes that are based on their ulti, like Earthshaker and Queen of Pain after her latest changes.
  
• Armlet of Mordiggian: generally a great early-to-mid pick for STR carries and autoattack-reliant STR heroes that usually lack attack speed but could certainly benefit from it, such as Chaos Knight, Legion Commander or Spirit Breaker.
  
• Skull Basher: good when one-on-one fights are ahead, especially on carries that end up having a lot of attack speed and tend to focus one target at a time such as Ursa, Phantom Assassin or Lifestealer. However don't build it if you're going to need a Monkey King Bar or it'll be a waste. It's disabled on built-in bash heroes (Spirit Breaker, Troll Warlord) and generally avoided on ranged heroes.
  
• Shadow Blade: for some heroes it might be a good option to cut distance using this instead of Blink if they can benefit from the bonus damage, such as Slark or Drow Ranger, although it's best kept as an escape mechanism on fragile heroes like the latter.
  
• Ghost Scepter picked up on ability focused and fragile heroes (Like Pugna or Skywrath) to counter esclusively physical nukes like PA blinking on you, Juggernaut and the like. Be careful on when you use it since you can't autoattack and you receive extra magic damage from spells during the effect. However you can still cast abilities, so you can use your crow control to neutralize the enemy and flee or wait for your allies. Profit!
  
• Radiance: used in some builds that rely a lot on perfect early farm to ensure great jungling capabilities in the long run and teamfight supremacy around the mid game. It's the risky alternative to Midas for heroes that can't use a Battlefury.
  
• Hood of Defiance: good defensive item if the enemies have much magic damage; perfect on tanks that could otherwise be burst down such as Pudge, Bristleback or Centaur Warrunner. Also obviously upgrades to Pipe of Insight, which is great for teamfights against magic users. Generally not a good pick on squishy heroes since they don't rely on tanking but rather on avoiding damage altogether and killing the enemy to survive.
  
• Blade Mail: core on heroes that will be focused in fights and/or are bound to take damage, like Undying or Legion Commander. Plus it's great if the enemies have annoying giganukers like Keeper of the Light, Lion or Skywrath Mage: they're usually quite squishy so they will likely destroy themselves just as much as the Mail carrier. Also it's great on tanks like Pudge and Bristleback if they get focused by farmed carries like Spectre or Antimage or anti-tanks like Lifestealer since it counters eventual lifesteal and gives enough time or damage to turn the tides.
  
• Vanguard: good early pickup for tanks and STR supports against a lot of autoattackers, plus it evolves into Crimson Guard which basically makes your team benefit from those defenses.
  
• Black King Bar: a must-get for squishy carries against disablers and heavy magic, plus it's vital to get on heroes that need to stay in the fight for long and that can't afford to be stopped once they go in. Squishy carries MUST have this against disables BEFORE getting into teamfights.
  
• Linken's Sphere: useful on heroes that are only targetable for a very short time (such as Weaver) or if you need to defend yourself against particular single target disables and comboes that you know will be focused at you. Obviously less useful if the enemy doesn't have many single target spells, but it's still good if you have a hero that doesn't likely build much regeneration nor Battlefury but still needs to be able to spam (Weaver again, on whom it's understandably a core item), although most ability spammers are INT based and thus do build mana regen sooner or later.
  
• Helm of the Dominator: taken by hard carries to stack ancients with a certain reliability (I've talked extensively about this item already, search for a thread on it on reddit.com/r/learndota2).
  
• Mask of Madness: picked up by carries that are hungry for attack speed and have some way to protect themselves from the incoming damage (carefully played Drow, Void, fotm Juggernaut) or heroes on which attack speed can give enough safety to partially counter the penalty (Spirit Breaker, Sniper).
  
• Diffusal Blade: picked up by carries that attack quite fast or melee illusion users (Lancer is both), plus its purge is great if you have debuffers against you or if you face heroes that rely on illusions to stay safe (Morphling, farmed Manta carriers, Lancer, Chaos Knight) since the purge instakills them.

• Necronomicon: good on both STR and INT heroes if you need pushing, offensive power or offensive vision (such as against a Riki), plus it gives survivability and mana. Obviously best on heroes that can empower their minions like Lycan or Invoker, and of farmed supports if farming power is lackluster.
  
• Dagon: on heroes needing burst damage (Nyx) or INT heroes that already have other tools they might need. If taken before counter/survival tools it's a greedy pick and usually doesn't pay off. Except on Pugna, he's always a beast with Dagon.
  
• Scythe of Vyse: good for stats for INT carries and well farmed supports, and also essential if there's an enemy that absolutely must not have its way into the fight, such as a farmed hardcarry or an initiator.
  
• Ethereal Blade: used on AGI heroes that have magic nukes, which are pretty rare (Morphling, Nyx) and sometimes on INT nukers, but it usually costs too much to be worth it more than a Veil for them.
  
• Monkey King Bar: lotta damage and True Strike: a pick up for autoattackers against PA and Butterfly/evasion users (doesn't work on Void's passive), plus it's quite good on autoattackers with a lot of attackspeed that can't use a Basher, including ranged heroes: Weaver, Windranger with Aghs, Troll Warlord...
  
• Manta Style: illusion users and AGI carries use it for stats and to turn the cards when they have to dispel something on themselves during a fight; also good to disjoint projectiles if you're about to get nuked by something like Sniper's ultimate.
  
• Heaven's Halberd: good to disarm pesky autoattackers and it's a good item on STR carries in general - it's basically Butterfly for STR heroes but you can also get in on supports if enemy carries are too farmed to be beaten in teamfights.
  
• Sange and Yasha: cheap all-around item for both STR and AGI carries, especially good for chasers (especially less tanky ones like Slark or Bloodseeker) since it both gives you movement speed and maim chance, together with survivability and attack speed. Some players dislike it since being it an all-round item it's not as effective if you have more specific needs, but it's generally a very good item for transition into late game due to its price (4100 when most late game items are around or above 5000).
  
• Desolator: usually the first autoattack improving item picked up by carries if there's no need for other specific UAM. Gives good raw damage and a good passive to focus down specific targets or towers.
  
• Eye of Skadi: UAM that stacks with lifesteal, yay! It gives very good stats, making you tanky while improving the autoattack. This is especially good for chasers, and the slow on the enemy's autoattack means you can generally win manly fights against autoattackers if you have enough damage. It's generally better to pick up some damage before it, but Slark is an exception because he nerfs the opponent and improves himself through autoattacking, so the earlier you have it on him, the better.

• Refresher: its uses are obvious. Good for any ulti with long cooldown that can change the tides, like Tidehunter (change the tides, heh), Enigma or Earthshaker. In any case, the only problem is the mana cost, which makes it a very late item because picking it up before having the mana to use the full combo twice is about as good as not picking it up at all.
  
• Daedalus: late game item for carries that have already stacked some autoattack items and don't need any (more) situational items. Core on heroes that rely on autoattack damage regardless of attackspeed, such as Kunkka or Ember Spirit.
  
• Butterfly: all-around late game item for AGI carries that would benefit from evasion and AGI more than crits, like Luna or Troll.
  
• Divine Rapier: it's obviously very risky to get since dying while carrying it will allow your opponents to have a chance to steal it. For this reason, it is generally bought on heroes that are incredibly difficult to kill after they have completed the rest of their build: Slark or Medusa are examples of such heroes and getting a Rapier when the rest of their build is complete could help denying your opponents any chance of recovering the match. Also, it would be a good bet for a carry to purchase it when losing the game: Rapier can give your carry the damage the team needs to win a teamfight against overfarmed opponents, and if you lose it to your enemy when you were already losing the game, it wouldn't make much of a difference.
  
• Abyssal Blade: upgrade from Basher, not much situationality: pick it if you have basher and you finished any other situational. You might want to get it earlier if you need a melee stun through BKB, such as against a strong melee autoattacker that is using an early BKB to win teamfights and get advantage.
  
• Shiva's Guard: usually a late pickup to consolidate armour defences and get a useful teamfight nuke/slow ability. Generally used by heroes that go deep into the fight like Doom, Sandking or other tanks.
  
• Bloodstone: every INT ability spammer's wet dream. It's costly, so it's usually reserved for late game, and it's not very useful if you end up already having a lot of mana regen before it, but there are exceptions.
  
• Assault Cuirass: late game item to consolidate physical defences in teamfights, usually picked up by tanks or fighting supports; if there's more than one of those, one gets this and the other gets a Shiva.
  
• Heart of Tarrasque: this is a consolidation item: apart from some exceptions, it's bought to make it hard to recover and come back when you already have the advantage. Buying this on a damage carry like Lancer will likely not make you win if you're already losing; if you're on a race against the enemy carry, building this will not usually be enough to counter the damage the enemy carry will have purchased instead of it. If you see no other way to protect yourself than raw HP hoarding, buy it. It's also used on tanks after they finished their main part of the build to make sure they are the most annoying as possible to the enemy and that they survive to participate in every fight.
  
• Mjöllnir: built through a Maelström. It gives attack speed and raw damage so it's good on everyone using autoattack really, but it's usually picked up by carries that especially need attack speed, such as Sniper, Alchemist, Lifestealer or builds including Basher. Bad idea on Troll since it goes over the atkspd limit and is thus a waste. It is a UAM, but the only moment when it doesn't stack is when the lightning is procced, so it's definitely worth picking up even if you already have other UAM, and don't let anyone tell you otherwise. You might get a Maelström early if you plan on buying this, and then finish other situationals before upgrading it.
  
• Satanic: upgrade of Dominator, useful on relatively squishy carries to make them more tanky and most importantly, allow them to stay in the fights for longer countering their low HPs though their high damage output. It's usually way better than Tarrasque on AGI heroes once they have the damage they need (and on Legion, since you'll have sick damage in the late game if you play well enough).

• Smoke of Deceit: this items makes run faster and it makes you invisible, even to sentry wards, towers and true sight, allowing you remain concealed even if you cast spells, until the duration runs out, you use your autoattack, or you come within 400 units from an enemy hero. This item is extremely versatile and is generally used to get into Roshan's pit without being detected by enemy wards, however it also has many more great uses: it can be used to gank the enemy team, invading their territory, but also just to get to a far point of the map when no teleport locations are nearby (for example later in the game when towers are down), or to get away from a dangerous place after having ganked an enemy, before reinforcements arrive.
  
• Dust of Appearance: this item reveals all invisible units and wards within range, giving enough time to neutralize an invisible enemy that happens to be nearby. It also prevents such units from entering invisibility, so it's safe to use even before an opponent has become invisible. Carrying this is always a good idea when there are invisible enemies in the game (Bounty Hunter, Riki...) and it's ideal to punish such heroes when they somehow give a clue of their presence, however it's usually also worth it to use it during or before an imminent teamfight to prevent invisible enemies from being at an advantage during combat, or even to put them down before starting the fight.
  
• Sentry Ward: this item gives true sight of invisible units around it for as long as it's up, but it also gives a limited sight of its surroundings for a brief time following its placement, making it ideal to destroy enemy wards even if they're placed in tall spots (a Quelling Blade can help melee heroes destroy wards that lay in unreachable places). Obviously, Sentries are also good against invsible heroes; compared to Dust of Appearance, their effects cannot be purged, but they're immobile and slightly more expensive to purchase. They are obviously good against heroes that can easily dispel Dust's effects (Weaver or invisible heroes with a Diffusal Blade) or heroes that only gain invisibility in certain spots of the map (Broodmother, Treant Protector). Other good places to place them are territories where carries are farming (in order to keep them safe from invisible gankers) and places where the team is fighting or is likely to fight soon.
  
• Quelling Blade: this item gives a very good damage bonus against non-hero units such as creeps, neutrals and Roshan, which makes it a very good option for early junglers or heroes that have difficulties having enough damage to take lasthits early on. It also deals a lot of damage to wards, so it can be used by melee heroes to deward in unreachable places, since its activation range is larger than melee range. Its ability to destroy trees is great to create paths in the jungle to farm more efficiently minimizing travel time or making camp stacking easier, but it can also be used to counter certain annoying abilities such as Nature's Prophet's Sprout or Treant Protector's Aghanim ability Eyes in the Forest (if true sight is available).
  
• Gem of True Sight: as the name suggests, it gives true sight of invisible units and wards within the carrier's sight range, which is clearly very strong, however if the bearer dies, it gets dropped to ground. For this reason, it is usually avoided if there is no safe carrier available and other options like Dusts or Sentry wards are preferred. If, though, there's a strong tendency to fight together, it's a great item to keep on tanks and other hard-to-kill heroes since it forces the enemy to focus such tough targets before making invisible heroes able to exploit their advantage again. If bought, it's also ideal to destroy enemy wards.