First came Achievements with the Xbox 360 and PS3 now has Trophies, but what exactly do these mean to you?
Personally I love them but I wouldn't say I obsess over them. They provide little challenges that can add to titles. I remember completing Stranglehold on the Xbox 360 (which didn't take too long) and started to look at the achievements. With no real online community, the achievements were the only thing that could flesh out the title and I attempted to earn quite a few of them (mostly I was successful).
Now with any title I find myself doing the same thing. That being said, I refuse to chase after achievements/trohies which I find to be dull. By all means, if I unlock them through the course of my normal play then fine but there's no way I will use the Gravity Gun to carry a small nomb through Half-life 2!