I prefer the term "achievement hunter", as it doesn't sound like I screw my Xbox begging for more gamerscore.
But yes, I try for achievements all the time. Even while I write this post, i'm trying to complete Cod: WaW on Veteran Difficulty, mainly for the achievements. I generally like getting achievements and increasing my gamerscore, but I won't go for achievements that require like.. 70 hours of gameplay, collecting every of a certain object (unless they're easy to find), and doing impossible things (like beating the main story mode in reverse). I also don't really like online achievements.