At its most basic, PvP in an MMO is just the ability - under set conditions - to punch your fellow players in the face. In a game world where open competition is the rule, PvP doesn't necessarily have to go beyond that. Give players the option to fight one another, and they will make their own story and set their own goals, or so the theory runs. Case in point: Eve Online, the sandbox in space.
But history has shown that goalless PvP can often fall flat on its face. When City of Heroes first introduced its Arenas, they didn't bring in the expected levels of player interest, mainly because there was no point to the fights. Without flags to capture, banks to rob or any other sort of goal to reach, the combat seemed aimless. Age of Conan has suffered from similar problems, though the PvP there is much more open. One way in which both these MMOs have tackled the aimlessness of PvP is to add 'minigames', in the context of which fighting has a point.
Should developers try to ensure that PvP has goals? Do minigames help, or do they just abstract the action away from the rest of the game world? Should players on PvP servers simply be given open PvP, and left to set their own goals?