Sometimes you are looking for unique skin which can be obtained only from specific quest or you want prepare for future Transmog UI (Wardrobe) where you will unlock ALL items appearances from completed quests in your characters, removed and obsolete quests too. If you play WoW for a long time you could forgot which quest you already did. Even if you know that quest is still available for you it can be part of long chain and you can have problem with finding which quests from it you already done. In this post I will show you how you can check if you already done chosen by you quest and another methods for recover lost items from completed quests (you can request item restoration to GMs in this case!!)
First of all you need to know which quest are you looking for. Lets say that you want to check if you have already done quest which name is : Showdown.
For those of you who do not know this quest offer as an reward mail head with an eye-patch skin. It is only one mail eye-patch available in game. If you already did this quest and removed it you can't get any other mail eye-patch for transmo.
To find out if your character already done this quest you need to have its ID.
1. How to get quest ID?
Lets say that you want to check if you have already done quest which name is : Showdown.
a) Go to Wowhead and search for your quest.
b) In your browser address bar you should see something like this:
Those number at the end will always be your quest ID. In the same way you can find NPC ID or item ID

2. How to get removed/obsolete quest ID and check old rewards? (many times removed quests and removed items from quests are missing or have incomplete info from wowhead)
a) Go to AoWoW - Vanilla WoW Database and search for your quest (database for vanilla wow items/quests only).
b) Go to LastWoW - TBC WoW Database and search for your quest (database for vanilla and TBC wow items/quests only). Useful for check removed quests/items from TBC as Zul'aman 70
c) In your browser address bar you should see something like this:
Those number at the end will always be Vanilla quest ID. In the same way you can find NPC ID or item ID from Classic WoW.
For example you can check old Naxxramas 60 Tier 3 quests or crafted Frost Resistance set quests on this page and you will not need buy Tier 3 from Black Market or craft very expensive Frost Resistance sets if you have completed these quests!!
Naxxramas 60 old quests: Naxx 60 removed quests
Zul'Gurub 60 old quests: ZG 60 removed quests
Zul'Aman 70 old quests: ZA 70 removed quests
Now when you have quest ID the funny part begins.
How to check if you done this quest?
There are few ways:

3. In game commands
You can use simple in game command or create macro with this code:
Where QUEST-ID should be replaced with your chosen quest ID. You can copy paste this line into in game chat or add it to macro so you will be able to come back to it whenever you will need it.
After entering this comand to WoW chat you can get two options 1 or nil. 1 - means completed and nil - means that you still can do this quest
There is also longer version of this command/macro (RECOMMENDED):
Where QUEST-ID should be replaced with your chosen quest ID. It shows a little bit longer results. For quest completed it shows: QuestCompleted:Yes and for not: QuestCompleted:No

4. Check your 'quest log'.
You can use this link:
For EU - http://eu.battle.net/api/wow/character/YOUR-REALM/YOUR_CHARACTER_NAME?fields=quests
For US - http://us.battle.net/api/wow/character/YOUR-REALM/YOUR-CHARACTER-NAME?fields=quests
Where: YOUR_CHARACTER_NAME should be replaced with your character name and YOUR-REALM with your realm name
So for example if your character name is Doktosqua and you play on EU server called Burning Legion your link should look like this : http://eu.battle.net/api/wow/charact...?fields=quests
If you will create this address in correct way you should see something like this:
It is list of ID from all quests you done on character you are checking. If you want to find out if your character done specific quest just search here for its ID. In your browser just ctrl+F and enter your chosen quest ID. If you can find it in this block of text it means that you already done this quest.
TIP: Use In game command/macro method too because a few quests are missing in this log.
5. Use other websites
There are websites like:
World of Warcraft Completed Quests Checker - Icy Veins
Which let you check which quest are still available for your character. It is quite easy to use. All you need to do is just enter your character details.
6. Ask Game Master
You can just simple write in game (or via website) ticket. Game Master should be able to assist you and check for you if you already done specyfic quest.
If you already done your quest it is possible that GM will restore your lost item. In Legion you will unlock item appearances from completed quests and you dont need restore these items BUT a few exceptions with no transmog items you can need request an item restoration to GMs.
Example: old brewfest steins for complete old feat of strength.
You can request old brewfest steins restoration if you have completed these quests:
Did Someone Say 'Souvenir?' - Quest - World of Warcraft --> 2007 quest
Say, There Wouldn't Happen to be a Souvenir This Year, Would There? - Quest - World of Warcraft --> 2008 Alliance quest
Say, There Wouldn't Happen to be a Souvenir This Year, Would There? - Quest - World of Warcraft --> 2008 Horde quest
Another Year, Another Souvenir. - Quest - World of Warcraft --> 2009 Alliance quest
Another Year, Another Souvenir. - Quest - World of Warcraft --> 2009 Horde quest
My 2007 brewfest stein restored in 2010:
7. Use addons
There are lots of addons which will just show you if you already done some quests. However usually they shows only quests in your current location or you need to know where exactly should be your quest. Anyway from my researches it seems that those addons can help:
Quest completist - Quest Completist - Quests & Leveling - World of Warcraft Addons - Curse
Quest hubber - http://www.curse.com/addons/wow/questhubber
I prefer other options and I'm trying to limit numbers of addons for performance purposes so I've not checked those particular ones. However I read lots of good opinions about them.
I do use addon called MogIt: MogIt - Transmogrification - World of Warcraft Addons - Curse it not only helps you with transmo but also shows skins sources. If particular item is from quest it will also let you know if you already completed that quest. This addon will not longer necessary when Legion pre patch will be release with new Transmog UI feature.
Important Tips:
- Remember that some quests have their Alliance and Horde version. Make sure you are checking right one.