They don't happen often, but when they happen, you remember them forever. My wife successfully taming Loque'nahk. The forging of my Quel'Serrar. Our first complete clear of Ahn'Qiraj. Even just sitting on my mount as the sun rose on Menethil Island and realizing I'd spent nearly an entire night with my then-girlfriend chatting in-between bouts of killing various and sundry things. Those little moments that make up the memories that keep people playing. One of the ones I've enjoyed the most in game, oddly enough, is a small set of linked quests available in the Dragonblight where you end up doing the same quest effectively twice, once as a mid 70's character getting help from your future self, and again as your level 80 incarnation going back in time to provide that help. I don't know exactly why but it's one of my favorite aspects of the game and one I've made sure to do over and over again.
Of course, they're not all good. One of my good in game friends delights in telling the story of the night my wife was patiently waiting for Lupos, a rare spawn worg from Duskwood, as she wished to tame said beastie for a pet. Lo and behold, as soon as she took a break for her biological means I linked a green drop in guild. As you can imagine, going on four years later I still hear about this from her when tempers are short. I've often wished Chromie would let me go back and stop that one, but so far no dice.
So now dear readers I ask you for your moments, be they great, terrible, or greatly terrible (or terribly great, even).