I care about achievements if they are conducive to the game, and they pose a challenge that is set up for me up front, with no fannying about.
For instance, you can get about 75 different Team Fortress 2 achievements by playing through a couple of maps with different characters. None of them seem to be anything worth fighting for. Trine achievements, on the other hand, as there were relatively few, were more rewarding to pursue, and the goal was set out in front of you, and weren't cryptic or abstract. "Complete X level without using your Y" kind of achievements, rather than "Get Up In That Bear's Grille!" which... could mean anything.
Actually, I don't wish to derail this thread by lambasting or praising the ubiquitous 'Achievement', which has single-handedly ruined games simply by being a vehicle to advertise themselves prominently on your Steam feed.
I'm still working through New Zealand Story on my Amiga, and trying to master all weapons/armour on Infinity Blade before the sequel comes out. I haven't reached the new content yet, having destroyed my game by going all "Game +" on its ass.