this is always a subject of importance to an MMO.
a brief explanation of the PVP types is below.
Open PVP: Think WoW on this one. Where you can walk around and gimp anybody you feel like, just cuz they're there. (assuming they're from the other faction)
Flagged PVP: Players can activate a PVP flag. if it is Active, they accept any duels automatically. If it is deactivated, you are unable to attack them unless they accept a duel.
PVP Arena: kinda like battlegrounds in WoW or Ballista in FFXI, where you enter an 'arena' where the PVP is set to open, or is based on teams.
No PVP: self explanitory.
I personally like Flagged PVP, it allows for options for the players, and still has that aspect of random fighting. Arenas are cool, and should still be in the game, but limiting PVP to arenas makes it cumbersome.