Depends on the game...
SWTOR and other MMOs with PvP, I PvP for fun.
CS:S, DoD:S and TF2, I like to win... but I usually don't, so I settle for focusing on a single target / player and taking them down as often and as brutally as possible. Otherwise, I play for the team. Sacrifice when needed, take the "boring" class in TF2 or DoD:S (basically whatever will do the most good at the time).
And in CS:S I just go on a shottie rage run, cause it's just that fun to pop around a corner and shottie someone's head off... Or the random knife-run.