I used to be an achievement whore. But after running afoul of a few achievements that were driving me up the wall trying to get, I finally had a moment where I asked myself, "Why am I doing this?" Now, I only try get them if they sound like something fun/interesting to do, or if I think I can get all of them without too much frustration. And if it's a game with many multiplayer achievements I usually don't bother at all.
Having said that, I can think of one positive aspect they add to games. Sometimes they impose a challenge that you might not otherwise have thought to try. Two good examples for me being "The One Free Bullet" and the one where you go through Ravenholm using only the Gravity Gun. I never would have thought to try either of those things, but they ended up being fun challenges.