At first I enjoyed them. In concept it makes sense that it adds replay-ability, it should only be a positive. I definitely have re-played a few games a 2nd or 3rd time through just to get the platinum trophy. That's a good thing. But I have to admit at times it also effects which games I feel like playing.
So I suppose that is a bit of a negative in that I might have delayed playing a few games because I "didn't feel like going for trophies", or because I got caught up trying to 100% something I might have set aside another game that was actually much, much better.
Fortunately I don't get caught up TOO much if I can't 100% game. Sometimes I will go all the way, and other times it's just not worth it. There have been more than a few games that I set out to 100%, but then when I discovered just how un-FUN the online or collectibles were, I ended up just abandoning the quest for 100% and moving on to something better. There's a few on my friends list that literally 100% *EVERY* game they play, and to me that would almost be torture. Sometimes you just have to walk away from a mediocre game. Especially those that are more time consuming.