Moonglade has a good post up about the pros and cons of achievements. Nowadays, achievements are everywhere, but when they were introduced to the game a while ago, they were seen as a great way for Blizzard to integrate an idea that had really taken off on Xbox Live (and that an impending competing MMO, Warhammer Online, was implementing for themselves). They were mostly seen as a benefit for the solo player -- even if you hit level 80 and nabbed some awesome gear, there'd be some optional fun for you to have in the future.
Since then, achievements have changed quite a bit -- I'd argue that they're actually more used in groups than in solo play, as raids check players for achievements when inviting them, and guilds use achievements to rate where their proficiency lies. There are certainly still lots of things for solo players to do (every holiday, achievements come to the forefront again), but titles and mounts have become the main goals there, not just optional points. As Moonglade says, instancing and checking up on what players have done seem to have become the main point of achievements. What was just a bragging competition on Xbox Live has transitioned to a real yardstick in terms of what a player focuses on in game and what they've done so far.
Is that bad? I don't think so -- Blizzard has done with achievements what they've done brilliantly with all of the other features of their games: borrow them, polish them, and then make them better. If you look through that old thread, most of the talk was about achievements pushing people to keep playing the game, and that happened, but I think one thing Blizzard has done is use achievements as a way to see what people have done so far as well: what instances have you run, what quests have you completed, what titles do you have already? There's lots more value to achievements than what any of us originally envisioned.