I like to get the ones I can get. Out of all the games I own, I only have 2 fully complete 360 ones (CoD 2 and ME2). PS3 I have 5 complete (RE5, Bio 2, Resistance 2, CoD WoW, CoD MW2). I mainly get them just for bragging rights with my friends. "Ha ha, I got that one and you didn't." We like to race each other to see who gets what first.
That being said, I do feel that they can take away from the game. Sometimes I find myself not wanting to play an old game because it has no trophies. I quickly slap myself for being silly and play it anyway though, but just that I have that thought is a disappointment.