I like to complete things, and achievements give me a good sense of what's out there.. And if I'm capable of getting all of the achievements for a game, I'll strive to do that (I'm not particularly good at games, so there are only a couple games which I've reached that level of completion, at least since achievements were introduced)
My friend whom I game with most tends to just see them as little cookies that he occasionally gets for doing interesting things, but will not in any sense strive to get them. I'm slightly more addicted to said cookies and will occasionally go out of my way to get them, and will remind him of simple achievements that he's passing by, and he just sort of looks at me like I'm nuts.
However, the score itself, I don't really care about. I'm not about pumping my score (although seeing my score as higher then my friends does sometimes make me smile), achievements are more of just a scrapbook of interesting things I've done. almost every one of them has a story attached to it that I can usually recall (at least the difficult ones), and even the not easy ones, the ones people would consider rote or boring (the ones people go THATS NOT AN ACHIEVEMENT RABBLE RABBLE RABBLE), they're just a way of saying "I was there, I beat this"
A game with good acheivement design, you'll get about half the achievements in a relatively full first playthrough of the game, then have to work relatively hard for the next quarter, and then ridiculously hard for the final quarter. To me, that's how it should be.