A great sense of accomplishment and pride comes with them, per say, an electronic trophy to wave around.
I'm an achievement whore. I force myself to play games sometimes, just for points. I don't care for shitty movie licensed games, but yet I still 1000 them out at the expense of my sanity.
At the same time, AP can introduce me to a game I normally would give you winks to a shit about. Two Worlds, for example. I won't elaborate on its redundancy or its lack of... well, most everything, but rather, in my quest to get that ridiculous end game achievement (Defeated the Grand Enemy - 370), I found myself actually having fun. Had it not been for that massive achievement, at least AP-wise, I dont think I would of dredged through that monstrosity.
The face value of a game can usually be determined by a quick glance of its AP list. Some games just give off a stink just by assessing the amount of detail and care (or lack thereof) that populate the list. At the same time, that can be a games saving grace and some of these games I've played I wouldnt of ever even thought of picking up, got played for the sole reason of harvesting their precious, sexy points.