I thought it was just boring games that needed such a gimmick, not the XBox360 as a whole. Apparently there are people who disagree with me, since a lot of people online seem to place some great value on their 'gamerscore' (as flawed a benchmark as it is).
Having achievements doesn't hurt anything, though. I just think that in a well designed game they are unnecessary (at best a minor feature). In principal they are an evolution of game design elements (such as hidden areas or bonus levels) and playstyles (speed runs, or lowest level finishes) that have existed pretty much as long as computer games. As a formal system, though, especially a 'tick box item' requirement, it seems more like a crutch for poor game design.