Before you start pumping Gambler's Dice or Loaded Dice into an item trying to get that affix you want, make sure it's actually possible for it to be on that item!

An item's material has no effect on its stats but can effect the price. Quilted Light Armor is worth more than Knitted, for example.

All equipment
The following affixes are available on all items:

• Enduring / of Endurance
  
• Insightful / of Intellect
  
• Ornate / of Worth (Max rarity Rare)
  
• Socketed
  
• Vampiric
  
• of Readiness

Weapon
Most affixes that are available to weapons are available to all of them, with a handful of exceptions.

One Handed weapons add 50% of your attack stat to their damage and Two Handed weapons add 62.5%.

Armor
Some affixes are restricted to certain armor pieces and/or weights.
Notes:

• Light Armor (Chest) and Light Armor (Robe) are different item types with some differences in affix access. (Light Helmets and Hoods are also different item types, but they have no differences in affixes.)
  
• The Bolstering prefix is exclusive to armor.
  
• A Lightweight Heavy Helm is the only non-Epic armor you can get with +Quickness!

Offhand

• Shield: Light Shields have 88% Heavy Chest Defense Rating and -4 Quickness, Heavy Shields have 166% DR and -8 Quickness. Mostly the same prefixes and suffixes, but only Light Shields can have of Discretion or of Dexterity and only Heavy Shields can have Deft.
  
• Parrying Dagger: Only offhand with access to Unerring.
  
• Talisman: Charm or Fetish.
  
• Light: Candelabra or Lantern. Mostly the same, but Lanterns can be Blinding and Candelabras can't. Blinding Lanterns are the ONLY non-Epic offhand item that can debuff.
  
• Tome
  
• Focus: Grimoire, Orb, or Skull. Only offhand with access to of Malice.

Ring
No special notes.

Back
There are a bunch of suffixes that only appear on cloaks in the back slot, but the skill tree specific back items have access to a couple affixes you can't get on cloaks.

UPDATE: With the release of Loaded Dice I'm now more confident in my data, although I haven't completely tested everything yet.

I created this simply by tracking which prefixes and suffixes I saw on which items while playing, NOT by looking at code or anything else. I did spend a bunch of time restocking shops and using Gambler's Dice, but while I'm confident that everything that I've listed as able to get a prefix or suffix is accurate it's possible that due to the randomness of this system I may have missed some items that CAN have certain bonuses. This is particularly true for accessories, which don't have a restockable shop I could keep refreshing. I did my best, but here are some items I wouldn't be suprised to discover exist even though I never saw them:

• Heavy Armor Chest: Lucky / of Hoarding
  
• Shield: Masterwork / Lightweight / of Speed
  
• Parrying Dagger of Aggression
  
• Candelabra: Blinding
  
• Cloak
  
  • Bolstering (Cloaks can have the two suffixes that trigger when you're hit, but I never saw this when hit prefix).
    
  • Restful (I saw the power after battle suffix but never the health after battle prefix, and it seems odd to have one without the other).
    
  • Runed (this is the only non-armor item I never saw the Runed prefix on).
    
• Battle Standard: of Malice / of Speed (these are both available to all other back items)
  
• Bandolier: Unerring (Quivers and Bandoliers have almost identical prefix / suffix lists. Quivers not having access to Mighty / of Strength makes sense but I see no reason not to have +Accuracy Bandoliers)

The new Loaded Dice item will cycle through the affixes on the item it's used on in a fixed order. If you want a specific prefix or suffix, this is an excellent way to get it without dropping tons of Gambler's Dice and hoping you get lucky. Note that Loaded Dice won't change a prefix to an affix (or vice versa), so if you have an item with a prefix and want a specific suffix first use Gambler's Dice until you get any suffix before you start using Loaded Dice. Here are the order in which the affixes cycle, skipping ones that an item can't have:

• Masterwork - Increased Weapon Damage or Defense Rating (Weapons and Armor)
  
• Mighty - +tier Strength (all except ranged weapons, tomes, foci, and quivers)
  
• Deft - +tier Dexterity (all except Maces, Magic Weapons, light Shields, Tomes, and foci)
  
• Ornate - Increased gold value (all non-Exotic)
  
• Lightweight - +2 Quickness (Heavy Armor)
  
• Vampiric - +3*tier Health Steal (all)
  
• Healing - +5*tier Healing Skills Bonus (Rings, Hand Armor)
  
• Soothing - +2*tier Health Regeneration (Armor, Rings)
  
• Padded - +10 Stun Evasion (Medium and Heavy Armor)
  
• Runed - +2 Power Regeneration (all except Armor or Cloaks)
  
• Consecrated - Removes "Restricted Skills: Divine" (One Handed Swords only)
  
• Greedy - +tier% Gold Find (all Accessories)
  
• Anti-Magic - +4% Resist Magic (all except Weapons)
  
• Venerated - Relic: +1 to Party <stat> (non-Exotic Weapons and Heavy Armor)
  
• Venerated - Relic: +1 to Party <stat> (non-Exotic Weapons and Heavy Armor)
  
• Enduring - +tier Endurance (all)
  
• Insightful - +tier Intellect (all)
  
• Unerring - +5 Accuracy (Weapons, Parrying Daggers, and Quivers)
  
• Lucky - +tier% Loot Quality (Light and Medium Chest Armor, all Accessories)
  
• Socketed - +2 Enhancement Slots (all)
  
• Staggering - On attack (75%), to enemy: -5 Quickness (2 turns) (Weapons)
  
• Blinding - On attack (75%), to enemy: -10 Accuracy (2 turns) (Weapons, Lanterns)
  
• Sundering - On attack (75%), to enemy: -10 Armor (2 turns)
  
• Restful - +10% Health After Battle (Armor, Rings)
  
• Bolstering - When hit (100%), to self: +15 Armor (1 turn) (Armor)
  
• Spiked - +2*tier Retaliation Damage (Rings and Heavy Armor)

• of Strength - +tier Strength (all except ranged Weapons, Tomes, foci, and Quivers)
  
• of Dexterity - +tier Dexterity (all except Maces, Magic Weapons, heavy Shields, Tomes, and foci)
  
• of Fortune - +tier% Gold Find (all Accessories)
  
• of Discretion - +Quick Retreat (Light Shields, Parrying Daggers, Cloaks, and Feet Armor)
  
• of Evasion - +2 Evasion (Daggers, Shields, Parrying Daggers, Rings, Cloaks, and Armor)
  
• of Malice - +1% Critical Hit Chance (Weapons, Foci, Rings, Cloaks, Quivers, and Bandoliers)
  
• of Readiness - +15% Starting Action (all)
  
• of Venom - On attack (75%), to enemy: (8*tier+tier/5) Poison Damage per Turn (2 turns) (Weapons, Quivers, Bandoliers)
  
• of Ferocity - On attack (75%), to self: +10% damage dealt (3 turns) (Weapons)
  
• of Respite - +10% Power After Battle (Armor, Rings, Cloaks)
  
• of Thorns - +2*tier Retaliation Damage (Armor, Rings, Cloaks)
  
• of Ease - +2% chance free skill use (Armor, Rings)
  
• of Reflexes - When hit (100%), to self: +15 evasion (1 turn) (Armor, Cloaks)
  
• of Agility - When hit (50%), to self: +12 quickness (1 turn) (Armor, Cloaks)
  
• of Endurance - +tier Endurance (all)
  
• of Intellect - +tier Intellect (all)
  
• of Worth - Increased gold value (all non-Exotic)
  
• of Recovery - +10*tier Bonus When Healed (Rings, Chest Armor)
  
• of Health - +4*tier Maximum Health (Armor, Rings, Cloaks)
  
• of Speed - +2 Quickness
  
• of Concussion - +5% Cause Stun (Weapons)
  
• of Aggression - +5 Enemy Attention (Weapons, Shields, Heavy Armor, Cloaks, Battle Standards)
  
• of Enervation - +5 Power Steal (Weapons)
  
• of Hoarding - +tier% Loot Quality (Light and Medium Chest Armor, all Accessories)
  
• of Reverence - Relic: +1 to Party <stat> (non-Exotic Weapons and Heavy Armor)
  
• of Reverence - Relic: +1 to Party <stat> (non-Exotic Weapons and Heavy Armor)

Note: An item with a built-in triggered ability can't gain another triggered ability from an affix.

An item can't have more than one of the triggered ability affixes - Blinding, Staggering, Sundering, of Ferocity, of Venom | Bolstering, of Agility, of Reflexes. Exotic items with built in triggers, like The Zephyr, can't have them at all.

Lucky / of Hoarding
It's not clear how loot quality adjustments work or the order different modifiers are applied in.

Masterwork
Uncommon Masterwork weapons and armor have the same Weapon Damage or Defense Rating as a rare version of the same item.

Vampiric
If you deal less damage than the listed health steal amount (due to damage resistance or killing the target) you only gain health equal to the damage you dealt. When using a multitarget attack, you steal health from each target you hit.

of Aggression
It's not clear how enemy attention works or how much impact +5 makes.

of Evasion
Your evasion is subtracted from an attackers accuracy to determine the chance an attack hits. Almost all boss monsters have inflated accuracy stats, usually around 145 but I've seen up to 195, so boosting evasion isn't as good as it might seem unless you get a LOT of it. Max evasion from non-Epic equipment is 20, so most of it will need to come from your skills.

of Venom
Poison damage by tier: T1=9, T2=17, T3=25, T4=33, T5=41, T6=50, T7=58, T8=66.
A possible formula from this data set is tier*8+roundup(tier/5) or roundup(8.2*tier).
Poison damage scales faster than weapon damage, becoming greater than the weapon damage of a one handed sword (ignoring the 75% infliction chance) at tier 7. Multiple instances of poison damage from equipment of Venom won't stack unless you're using the Miasmic Embrace relic. Most Undead and Constructs are immune or resistant to poison.

Consecrated
A Masterwork One Handed Mace will do more damage (and have +3% Cause Stun) compared to a Consecrated One Handed Sword. I haven't run the math, but a Mighty mace is likely also always better than a consecrated sword.

For the sake of completeness I will mention that because maces can't get the dexterity increasing prefixes/suffixes, if for some reason your Divine character wants a one handed melee weapon that deals strength damage but has a bonus to dexterity your only option is a Consecrated Sword of Dexterity.

of Health
of Endurance gives more the same or more health per tier for every class except Mage and Mage Lord, and also benefits anything that scales off endurance.

Masterwork Wands & Staves
Non-physical attacks scale their damage directly off Intellect, ignoring Weapon Damage. The weapon damage increase from Masterwork therefore is wasted on characters who use magic or holy attacks, unless they frequently use basic attacks instead of skills.

Venerated / of Reverence
An item with both the prefix and the suffix gives two +1s. Once you have access to regular relics from exploring ruins, wandering merchants, and lurkers, the +1 to one or two stats from relic equipment is no longer worth a slot in your reliquary.

Once you're far enough into the game that you can easily come by whatever Rune equipment enchantments you want, these affixes are outclassed by using the Socketed prefix (adds two enchantment slots, available to all items) and the appropriate Runes.

Suffixes are technically not outclassed on rare equipment where you have both a prefix and a suffix, since Socketed only replaces a suffix in that it lets you choose a different one, but they are directly outclassed on uncommon, storied, and exotic equipment that can have either a prefix or a suffix but not both.

Runes cost 1,500 gold when bought from the Enchanter's Table in Savantir.

Anti-Magic
Socketed with two Runes of Warding gives +6% Resist Magic instead of +4%.

Masterwork (Armor)
I suspect that two Runes of Protection for +2 Armor will beat the increased Defense Rating from the Masterwork prefix, but I haven't run the math on this yet. Depending on how Armor is Calculated from Defense Rating, the percentage increase to DR may also start beating the flat +2 directly to Armor at higher tiers.

of Readiness
Socketed with two Runes of Vigilance gives +24% Starting Action instead of +15%.
Note: A Socketed Ring of Readiness with four Runes of Vigilance gives you +63% Starting Action.

of Respite
Socketed with two Runes of Restoration gives +14% Power After Battle instead of +10%.

Socketed with two Runes of Power is better than Runed ONLY if battles lasts five turns or less AND your power is completely refilled between battles AND you're spending all your power each battle.

Once you reach the endgame and can start enhancing your gear with epic Shards, equipment with the Socketed prefix renders a bunch of affixes subpar. As with Runes suffixes technically aren't strictly worse on rare items, but at this point you're probably using Exotic gear.

*The Health Steal granted by Shard of Eridos does NOT scale, so going purely by Health Steal amount a Vampiric item of tier 4 or higher is better than an otherwise identical Socketed item with two Shards of Eridos.

Stat Increasing Affixes / of Health
Socketed with two +10% shards is better than a prefix that gives a flat tier-based increase to that stat when that stat/5 > tier. So a tier 7 Mighty item only gives a higher Strength bonus than two socketed Shards of Skosyr if your strength is 34 or less, for example.

Runed
Two Shards of Euphia give the same amount of power regeneration but add +20% Intellect.

Lightweight / of Speed
ONE Shard of Nidal or Sarilas matches the speed bonus and also gives +10% Endurance or +20% Starting Action.

Restful / of Respite
ONE Shard of Callara doubles the health and power after battle of these affixes.

Soothing
Two Shards of Eridos grant more Health Regeneration as long as your Health > 20*tier.

of Malice
ONE Shard of Dilaera matches the crit bonus and also grants +15% crit damage.

of Readiness
ONE Shard of Sarilas gives a higher Starting Action bonus and also grants +2 Quickness.

Values here are estimated based on what calculations I've managed to figure out, and may not be entirely accurate.

Unerring
Accuracy seems to increase by 1% every 20 points of Dexterity, so at 500 Dex the +5% accuracy from +100 dexterity granted by two +10% dexterity shards will match the +5% accuracy from the Unerring prefix.

Padded
I haven't figured out the Strength to Stun Evasion calculation yet.

Restful / of Respite
+20 Endurance = +1% Health After Battle, so +200 end matches the +10% from this prefix. That requires two +10% endurance shards and 1,000 endurance. Same calculation for Intellect and Power After Battle. A Shard of Lairit (+10% end and int) will match a Shard of Callara (+20% health & power after battle) at 4,000 endurance and intellect.

of Concussion
I haven't figured out the Strength to Cause Stun calculation yet.

of Ease
I haven't figured out the Intellect to Free Skill Chance calculation yet. (6=1%, 60=2%, 100=3%...)

of Evasion / of Reflexes
I haven't figured out the Dexterity to Evasion calculation yet.

of Recovery
Assuming the +10% Bonus When Healed is 10% of your max health, two Shards of Vornis grant a higher bonus when your health > 50*tier.