Specifically my WoW pvp habits ;
While playing on a PvP server, in PvP areas like battlegrounds, or lake wintergrasp, or while in a world PvP raid, i would kill anyone near my level, occasionally just anyone regardless of level. Outside of PvP areas, I wouldn't bother with PvP at all, UNLESS they are killing a mob I want to kill, or taking ore I want, or engage me first. Even if they are obviously in trouble, with mobs, I probably won't help them. I tend to do OK at pvp, just from studying it, but I am not passionate about it at all. It's a benefit to be able to kill someone who is taking what I want, but it's also a benefit to be able to go afk in more places in the game world without worrying about losses. There's a bit of thrill in danger, but overall I can't be made to care about consequence free PvP.
I have PvPed in Eve Online, WoW, Age of Conan, LOTRO, and Warhammer Online.
I have a more aggressive stance in Warhammer than the other games, because it's 100% intended to slay the other faction at all times - I would pursue any opportunity for a kill in that game. Conan and Eve are FFA type games, where there's no one you can assume is friendly, even your countrymen, but by the same token they are not automatically enemies. I tend to assume that a person is out to kill me, in these games, and practice a lot of avoidance techniques. Specifically in Eve the death consequences are so high that it can cause a lot of drama if you attack someone without warning. In WoW, because I am motivated to play by PvE concerns, I don't care to PvP much, especially since I never ran around PvP specced. Lotro is 100% pve outside of a specific area, but while there I would kill anything I was capable to kill.