Achievements are essential! There are multiple reasons that I am an achievement whore.
1. Gamerscore = bragging rights
2. Achievements help measure completion of a game
3. Some clever achievments actually change the way I'd play a game
4. Closing out a game has a whole new meaning and is much more definitive
5. After gaining 50 points in one day, it's usually a good sign that I played enough that day :)
6. I like to be rewarded. Avatar rewards, gamer pic rewards, mental pat on the back rewards. Yeah...
I'm sure there are more, but I think it's safe to say that I am indeed addicted.