Personally, I find achievements to be stupid. Wooo, you finished level 5, so here's an achievement. Weeeeeee, you killed 800,000,000,000,000 enemy foot soldiers who are all identical and are killed with one bullet, here's an achievement.
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The August 2010 issue of PC Gamer has a guest editorial which addresses this somewhat. It's written by Mikail Yazbeck, one of the designers of Mount and Blade: Warband.
He describes what he sees as the proper way of using achievements: as a way to give free-form games the same sense of gratification which linear games have, to get players to play the game longer and in different ways.
However, applied differently, they become the way by which the free-form game becomes linear. They become the designers way of forcing the player to play a certain way.
I think he has an interesting take--it might be worth looking at.
I take the "it gives me a reason to play longer" approach to it. Before achievements I would finish a game and be done with it. With achievements I play through the game casually to enjoy it and once that's done I see which ones I never got by dumb luck and work towards them.