I think my really proud moments about this game were back in vanilla, which doesn't mean I was super awesome back then or those proud moments would be connected to my biggest achievements in vanilla or WoW.
Over the years I have become quite good at the pve aspect of this game (I am terrible at pvp), during burning crusade I managed to repeatedly get really good dps rankings on bosses which continues to this day. I also began to clear all the available pve content when it was current, without increasing my time-commitment to WoW (in fact, it decreased slightly), so over the course of this game I would say that I constantly improved from really being not all that great during vanilla.
HOWEVER... I think my proudest moments in WoW were at the times when I was really bad at this game, were not quite aware of it and could really be proud of little things like mounts.
I think my proudest moment was when I looted my first epic item from Molten Core (felheart girdle, random trash drop).. next to that was acquiring a Tier 2 set helmet from onyxia. I would literally hang out in pug-dungeons afterwards, rubbing my first awesome shiny epics into the faces of those non-raiding uber-noobs.. until I had to log off and go to school next day.
When the people in said pug-groups would ask me why I was running stratholme with my epic gear, I would even respond with bullshit like "you know, as a raider you need to seek for constant improvement" and dumb stuff like that
Yep, I'd say that this was the time I was extremely proud of my ingame achievements although they were crappy and little ones and I was far from being a good player. I think being only 16 years old back then plays a role in this, too.
Nowadays, being quite a bit older and actually having raided on a high level for quite some time it's nothing that makes me super proud and there is no need to pose with my shiny heroic raid loot and tell people about my awesome dps-rankings in game. It's actually more about just playing a game.