If you're talking about the official "Dragons" (not including Drakes, Drakonids and various other Dragonkin) currently in World of Warcraft that you are able to kill, they are as follows:
Nefarion - Blackwing Lair, located in Blackrock Moutain
Onyxia - Onyxia's Lair, located in Dustwallow Marsh
Vaelastrasz - Blackwing Lair, located in Blackrock Moutain
Azuregos - Azshara
Eranikus - Spawned by an event in Moonglade (you can also fight his shade, which is located in the Sunken Temple, Swamp of Sorrows)
Taerar, Lethon, Ysondre and Emeriss spawn randomly throughout the world in the following places:
The Hinterlands, Seradane
Duskwood, The Twilight Grove
Feralas, Dream Bough
Ashenvale, Bough Shadow
You can also attack Anachronos near the Temple of Time in Tanaris, but once he reaches a certain % of HP, he temporarily despawns.
The reasons you kill these dragons are simple: challenge and epic loot.
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Profile Ghwrin.60.Gnome.Warlock (Tichondrius)
Ghwrin.60.Human.Warlock (CB PvP)
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