One of the best things about the Xbox 360 is the achievements that are built into every game. They give you a little extra incentive to play a game longer than you would have in the past to earn an achievement and add a few points to your gamerscore. Yes, your gamerscore is meaningless, but there is nothing quite as satisfying as playing a game and hearing that little sound effect and an "Achievement Unlocked" window appear.
LOTS of Xbox Gamer Score #shorts
One of the best things about video games is that you can unlock new items. Fighting games, racing games, and FPS are great at constantly rewarding you with new trinkets and characters and such. Achievements are an extension of that. You are constantly rewarded, which only keeps you playing longer in the hopes of earning something else. And it all adds up to a nice tidy gamerscore that you can share with your friends.
Good: Good games to improve your gamerscore reward you for completing the game, performing specific in-game tasks, or achieving goals within reasonable limits
Bad: Bad games for improving your Gamerscore are games that require a long time investment, top online leaderboards, or feature mostly online-only achievements.