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.
Agreed, achievements should always come as a reward for doing something interesting and fun in the game, not be a way to artificially increase the length of the game by giving silly and unreachable objectives. A perfect example of a game with flawed design that used achievements to save the day is Assassin's Creed. Given the (very) repetitive nature of the game, and the gimmicky achievements included in the game (find all "flags" in a city, kill every Templar, etc), I think it is a safe bet to say that these were most certainly after-thoughts, added at the last minute when the developers realised their game was a bit too empty. Actually trying to collect all flags is nothing but a chore.
Back to our beloved Divinity II, I can tell you that you will never have to go out of your way to get the achievements, some will come to you automatically as you reach certain key moments of the main story, and others for finding secrets and easter eggs as Lar mentioned. Don't worry, we won't make you kill 200 goblins or play for 24 hours without pausing
Our achievements improve the gameplay, they don't compensate for it!
