I dont know about quitting all together, but I'm more about starting a game playing for awhile, and move on to something else. It might be another system all together. The compelling factor of " I must finish this game!!!" never really grabs me. Lol, maybe I'm just lazy!
Like with Rock band. I have my 7 or 8 songs I really like to play. I dont really care if I finish the whole game.
As far as beating a game on the 360...I guess it's the games I have. Most have multi player. Which is what I like. I like to play as a group more than I do solo. So beating a game never really comes up. I have more racing games than other genres. And racing is, well, racing. I guess finishing a season or a collection circuits would be finishing a game...but I just like to throw in the game, hit the throttle, and goooooo!
If I have to pick thou, I guess yes...I am a game quitter.
Note: Games I have finished with friends...Lost Planet, Call of Duty 4, Conan. We take turns doing a mission, then pass the controller. Or, if you failed a mission, pass the controller.