It depends on the achievement really. I'm really proud that I got an achievement for beating Mass Effect on Insanity, as I found that pretty challenging and an achievement in itself. In the long run though, they don't really matter, although I have found myself renting games that my friends have played so that I could beat them... But I don't get bent out of shape about it.
For me, they do add more length to the game, if the game was already fun to begin with. For example, I have no desire to go achievement hunting in Mirror's Edge, because that game was frustrating. I got all the basic ones and maybe 2 or 3 extra and I'm fine with that. On the other hand, I'm actively working to get all the achievements in the Mass Effect games, as those actually provide some bonuses (mostly in ME1; ex. getting 150 sniper rifle kills allows a new character w/o sniper rifle training at the start to select that as an extra ability), as well as the game actually being fun.