I've engaged in team killing because:
1. Fellow player killed me and the feud is on (this can get really crazy fun)
2. By accident, sort of (noobs stop running into the middle of things and learn to take cover)

The list was pretty awesome but there should be one for that person who treats the game like a chat room instead of a killing field.

 

Exploitation. Usually only after getting thoroughly frustrated with playing normally.

If I die and lose a bunch of progress because a game's checkpoint system is retarded and I just can't be bothered to do it all again....yeah. (This is why Skyrim's quicksave/quickload is the best thing ever)

 

Team killing only ever accidentally until someone has TK'd me deliberately/multiple times and I am annoyed and retaliate.

I used to AFK for up to 15min at a time when I used to play MOH:AA. Australia didn't have many active servers when I started playing and my favourite one was almost always full (online friendly acquaintances favoured that server, favourite game mode, etc). If I left my computer for the bathroom, to quickly nab some food, or once or twice even a quick shower, I'd hold onto my spot in the server by sitting on spectator mode.

 

I've probably done all of them, at some point, since I play a lot of online games. I have since I was, eh, quite young.
Some were in good fun. Some ...well, not.

 

This ^.

If a particular player is annoying the shit out of me (Mortar users in BF3 are a perfect example of this. Fuckers are the anti-snipers.), I'll make it my mission to find that person, kill them in a horrifically embarrassing way, and then teabag the hell out of them.

I generally only TK exploiters and glitchers, real ones, not just having an OP build.

I haven't ganked lowbies since Galaxies, but they were Rebel scum and I still feel no remorse.