Quake and Counter-Strike have probably done more to popularize online play than any games yet, even though they are purely the domain of FPS fans. Quake could be played cooperatively, but given the severely limited artificial intelligence (AI) of the day, playing against other players was the real challenge. No more watching hordes of mindless enemies run around a corner directly into the spray of your plazma gun. Sure, AI has improved over the years, and in a few cases it's even been made too good, but PvP is not just about difficulty settings. AI has, so far, always become predictable, whereas you never know what insane move a human player is going to try next. Perhaps more importantly, humans make mistakes.
For many of us, competing against a machine simply isn't as "real" as competing with another person. It's more difficult for me to get emotionally involved in the game when I know that my computer opponent isn't getting emotionally involved. The boss monster at the end of the level may look big and angry, but he's not really angry, he's merely following the script. Similarly, playing chess against a computer can be extremely challenging, yet most people don't find it as exciting as playing against a friend.
PvP seems to be a natural fit for shooters, many of which have evolved into sensational contests of controller dexterity, reflexes, and teamwork at the same time.
The implementation of PvP in statistics-based RPGs, however, has always been received with mixed feelings and surrounded with controversy. Games such as Ultima Online, Lineage, and Shadowbane, have, at one time or another, earned notoriety for the sheer brutality of their PvP rules, allowing high level characters to prey on low level characters, and offering little by way of refuge. This can be a rather frustrating experience for new players, who must find their way in a world full of hostiles they can't possibly compete with.
Subsequently, a lot of RPGers associate PvP with the rampant "ganking" that is not uncommon in certain games. Ganking is a term that refers to killing another player's character, particularly when that character has little chance of defending themself. Frequently perpetrated by rogue classes, it can quickly degenerate into an attempt to ruin the game for another player by killing them repeatedly, or "corpse camping," which it would be a stretch to describe as "fun" for either party.
Most MMORPGs have servers with different PvP rules to address this. World of Warcraft gives you a choice between playing in a world that allows open factional PvP in certain areas, or playing on a "normal" server, where PvP is entirely consensual. Asheron's Call offers Darktide; a shard that allows everyone to attack to everyone, and calls for a WoW server with similar rules surface on the forums occasionally.
So, given that players usually have a choice, why play on a PvP server? At it's best, PvP is not just about ganking other players; it includes politics and teamwork. If vulnerable characters are being harassed by higher level characters from an enemy faction, they should be able to call in reinforcements from their own faction or take some other recourse. Ideally, actions have consequences that get other players involved. Territorial control is one way to make a battle more interesting and rally players around game objectives. In good games, players are given better ways to entertain themselves than corpse camping.