I like achievements a lot. I generally do not care about the global achievement score. However, I really enjoy it in individual games I like. For lack of a better term, it is almost an RPG aspect to games. I always did this on 8 bit RPGs. I have to collect all 150 pokemon, collect every hidden item, and do every trainer battle. In Phantasy Star, I have to buy the best weapon and armor. I will spend pointless time grinding for that stuff when it is not needed to beat the game.
That's what achievements are to me. If I like the game, I don't want to just beat it. I want to make sure every rating or power meter is at its highest. Achievements are just the next progression of career modes introduced in 16-bit gaming.
Now, if I don't like the game, I won't even get the achievement for beating the game. Because, again, I don't care too much for the global score. It's kinda neat. But nothing big.