You know, you can turn off trophy notifications if you dislike them.
I personally love them, especially if they are challenging (I did 100% Platinum stuff like DoA5, UFC, MvC3, Super SFIV).
I like going for trophies but I don't usually get out of my way to get them, I only really try to 100%/Platinum my favorite games (usually fighting). I do play games without achievements and trophies but I'd rather have them.
Having a list of everything I ever played on PS3/PSV/X360 (soon PS4 and XBONE) is really nice even if my completion rate sucks.