Player Kill
The term Player Killing, Player Killer, or PK refers to non-consensual PvP. The verb of killing players is usually called PKing, and someone killed is PKed. A Player Killer is usually just referred to as "a PK".
PKing is generally non-consensual, and often takes the form of sneak attacks, often performed with the aid of deception, cheats, or hacks.
There will not be any support for PKing in Diablo III, since all PvP is going to require player consent. How exactly this will work has not yet been disclosed publicly.
PKing was a major issue in Diablo II, with passionate arguments on both sides of the issue. The D2 team thought it was worth including in the game (via the "hostile" button), but the ease with which hostility could be declared was limited in various post-release patches, which gave unsuspecting characters more time to flee or prepare themselves before a PK could swoop down upon them.
Though Diablo I and Diablo II allowed for non-consensual PvP, most modern RPGs do not. Duelling is almost always allowed, but each player must agree to it, either at the time of the duel, when joining the game or entering the PvP-allowed area, or sometimes upon character creation or realm assignation.
PKing will not be a part of the game in Diablo 3, since the D3 Team has said there will not be non-consensual PvP. They have not yet released details on how PvP will be regulated, but it's widely assumed that it will only be allowed in special, "arena" type games. Many players hope for PvP ladders, rankings, and other bonus features to facilitate duelling, but the D3 Team has been entirely mum on those issues.