Originally posted by tf2 wiki:

Unique quality is the item quality assigned to items which can be found through random drops during gameplay, obtained through achievements, crafted, or purchased from the Mann Co. Store.

Originally posted by tf2 wiki:

Vintage is an item quality used most commonly to designate previously Unique items obtained prior to the Mann-Conomy Update, where it was introduced. This was to increase their appeal in trading.
In the March 15, 2011 Patch, several expensive crafting recipes were modified to be cheaper. To recognize items that had been crafted while the recipes were expensive, Valve upgraded them to Vintage quality.
In some cases, items that have been re-granted to users by Steam support (after being either accidentally deleted or stolen) were assigned Vintage quality.
Vintage quality items are purchasable from the Steam Community Market

Originally posted by tf2 wiki:

The Genuine item quality was originally introduced alongside the RIFT promotion as a way to allow items obtained through participation in a cross-game promotion or an in-game event to be distinguished from the same items gained via other methods - such as through the random drops or via crafting.

Items with the "Genuine" quality can be strangified, but their names (and the item's icon in the user's backpack) will keep the "Genuine" quality color instead of changing into the "Strange" quality color. Strangified "Genuine" items will also still display the item's rank as a normal "Strange" quality item would do. "Genuine" quality items can be obtained via trading, and are also purchasable from the Steam Community Market.

Originally posted by tf2 wiki:

Strange quality is an item quality available for weapons, cosmetics and taunts. Methods of obtaining Strange items include:

• Unlocking a Mann Co. Supply Crate containing the item,
  
• Using a Strangifier on an item,
  
• Purchasing the items from the Steam Community Market,
  
• Earning Botkiller weapons or Australium weapons from Mann Up mode,
  
• Trading with other players for them.
  
  Strange weapons track kills or other various events (see Notes below for exceptions), and records them as an item attribute, allowing the count to be viewable by other players and the owner. Cosmetic items with the Strange quality track the number of points scored while wearing the item. Strange items are awarded new ranks as their counters increase, with the rank affixed to the beginning of the item's name. Each time a Strange item reaches a new rank, the event is announced to all players on the server with a message in the chat box; A notification pop-up will appear, accompanied by a sound, but only for the player the strange item belongs to.
  Decorated weapons with the Strange quality will have a "Stat-Clock" placed on the weapon that increments in real-time.

Originally posted by tf2 wiki:

Unusual quality is an item quality used on cosmetic items, taunts, and weapons. Unusual items have special attached particle effects, and are considered to be some of the rarest items in Team Fortress 2. There are currently 416 cosmetic items that can have one of 66 total effects, 18 taunts that can have one of 15 total effects, and 10 weapons that can have one of 4 effects. The only methods of obtaining an Unusual item are by unlocking a Mann Co. Supply Crate with a Mann Co. Supply Crate Key (at an about one in one hundred, or 1.00%, chance of unboxing.[1]), purchasing one on the Steam Community Market, or via trading.

Unlike regular items which can only be obtained from specific crates, any item obtainable in Unusual quality can be unboxed from any given crate, however the particle effects obtained depends on the series of crate the unusual item was obtained from. So, to unbox a cosmetic item with a "Series One" effect, a "Series One" crate must be opened, and so forth.

Originally posted by tf2 wiki:

Haunted is an item quality designated for Halloween-themed items. Many, but not all, Halloween items have a Haunted version.
Costume pieces from the Very Scary Halloween event could be obtained in Haunted quality if a Haunted Halloween Gift was found in the Underworld section of Eyeaduct, or rarely from a Halloween Goodie Cauldron. During the Spectral Halloween Special, items unboxed from Eerie Crates were Haunted, with the exception of the event in which an Unusual hat was found instead.

There was also a chance that a Voodoo-Cursed Soul can be obtained in Haunted quality when a player used a Pile of Curses. The Halloween Gift Cauldron added in Scream Fortress 2014 is guaranteed to have at least one of the items from it be in Strange Haunted quality. During Scream Fortress 2015, the Merasmissions had a chance to reward the player with a random Halloween item from the previous Scream Fortress events to be Haunted, the Soul Gargoyle also had a chance to give the player a Haunted Halloween item from the previous Scream Fortress events when the Halloween Transmute was done by the player, the player would also receive a bonus Haunted item if the Halloween transmute was done 10 times.
Haunted versions of items are visually and functionally identical in-game to their Unique quality counterparts.
Haunted quality items are purchasable from the Steam Community Market.