I think they were an ingenious innovation. I think they're great for gamers and retailers alike. A gamer wants achievements because they play to what gamers inherently love, numbers going higher for completing more things in a game. It's almost like adding an RPG to element to your overall gameplay. Not only this, but it adds a lot of replayability to a game. It's great for retailers because achievements push more copies of games. I read a poll, I believe on Joystiq, where owners of both the 360 and PS3 overwhelmingly chose to get GTAIV on the 360 simply because of achievements.
I also think, as long as people don't get too competitive with achievements, they can be a great bonding point for gamers. They can instill friendly competition, and also encourage gamers to work together to get the same achievement. I've even sometimes worked with someone to help them get an achievement, say in Guitar Hero 3, and then had that person help me get the same achievement (or a different one) in exchange.
My question, then, is why do I constantly see people in forums dissing achievments and saying if you have a lot of achievement points you have no life? If you want to integrate achievements into your gameplay, great, you get all the advantages mentioned above. If you don't, great. It doesn't really matter. Why do you have to berate people who like working toward difficult achievement points in games?