I could never relate to the Achievements craze, but it has a real grip on some people. I PM'd someone on my Friends list to ask if the game they were playing was any good, they replied 'nah, rubbish, just playing it for the Achievement points then taking it back to the shop.' I don't know what it is about them... I never cared personally.
Although I've never played a game simply for the achievements, I do understand the appeal. My game of choice is Left4Dead 2. I've earned just about every achievement that you don't have to consciously work towards and it is cool to see that you've done something the developers deem an accomplishment in your gameplay. It shows improvement and allows you the opportunity to see how you stack up against other players. In the end it's a little about status and a little about a feeling of personal growth.
Dunno about playing un-fun games for achievements, but Civ V (for example) has achievements to push you to explore every part of the game. Going through them has me working on crazy win conditions, the 1-city challenge, different leader strengths, etc. Adds a bunch of replay value for a pretty small amount of extra effort.
