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".
Description
PKing is generally non-consensual, and often takes the form of sneak attacks, often performed with the aid of deception, cheats, or hacks.
PKs might also be duelers interested in PVP, but the term is more often used to describe players who force non-consensual combat; sneak attacks and ambushes and other behaviors that can be considered griefing. Diablo II allows PKing, though there are various limits placed on when, where, and how players can go "hostile" to each other, as well as damage penalties and other controls to level the playing field. Read more about those here.
Diablo III
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.
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.
Diablo II
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 or Not?
There is always heated debate about how much, if at all, RPGs should support PKing. Almost no one argues against dueling, but whether the PvP combat should ever be non consensual is the big question. Most early RPGs allowed it, most modern ones do not. Players must select PvP upon character creation, or by the realm they play on, or by the game type they join, but in almost all cases it's possible to avoid PvP entirely, if a player so desires. World of WarCraft does not, and Diablo III will not, allow non-consensual PvP.