On PC I never bothered to complete everything. I just played the game and finished it. The exception was BF2142 where I just needed about 3 more achievements to have full house. When I started PS3 this changed. I now rarely play a game that I will not go for the platinum trophy. I donr have much time, so my plat count is still low (15 refer my sig) compared to some of the other guys. I take my time and it takes a few months for me to complete a plat but I enjoy it. I consider myself a trophy completionist in that respect.
I'm 3 trophies away from getting the Platinum for Red Faction: Armageddon. I don't usually go for Platinum Trophies (Borderlands is my only one atm), but I just enjoy the game so much that I can't stop playing it. I've already finished it once on PC and once on PS3 and I'm currently about 75 % through my second playthrough on PS3, after that it's one more time on Insane difficulty and then I should have the plat.