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.
When I made my full raid wipe on Festergut pulling unintentionally with my mage.
My proudest moment was back in the ol' good LK times when my guild and me, two days before Cataclysm, finally killed Arthas in 10nm (for us was an achievement) when two of our three heals were dead and only two dps were there to kill Arthas (me and a sp friend). We ignored the RL, we ignored the spirits, the heals and the tanks, we ignored everyone and just used everything we had while we run on the platform 'til we killed him.
Server first Al'Akir, Cho and Nefarion Heroic. Also killing C'thun for the first time in Vanilla. On a more social scene, managing to get almost everyone a ZA red bear mount. Unfortunately 1 person missed out and I have never forgiven myself for not making enough runs.
Back in teir 11 I was in the underdog group in the guild with two groups. Well... our raid team joined their guild ect. Starting halfway though the tier dealing with them every once in awhile trying to snipe a member of ours when they didn't have enough for that night. Half of that group hated us even though we were a nice bunch. However we beat them on heroic Chimeraon kind of out of the blue and I have never seen a group of people rage so hard. They ended up kicking us out of the guild then disbanding giving the guild back to us after a month.
Making a successful 25man raiding Guild from scratch at the beginning of MoP (while most people considered 25man a impossible to create)
Now I have a very rare Guild with Raiding 2x 25man groups (8/14H and 14/14N) and Im still proud for what I did.
I would have to say my proudest moment in WoW just came recently on what looked like a wipe on Paragons. A Shadow priest and I were all who remained with the 3 final bosses. Pushing the enrage timer to the bring and cycling every cool-down on the planet as a Protection Paladin the two of us beat the encounter with 3 seconds to spare.