If an MMOG advertises player-vs-player gameplay, I don't have to wonder what type of PvP they mean. It's dueling. It might be between two players or two factions, for money or for roleplay value, but its basically combat with the opponent's physical defeat as the goal.
Don't get me wrong, I think that kind of PvP combat can potentially be a ton of fun. Though it's been a while since I looked that way, I was big fan of the original concept for Trials of Ascension. I also enjoyed eliminating Rebel scum for a while in Star Wars: Galaxies.
But why haven't MMO developers pushed on into other forms of PvP? The "versus" in PvP denotes competition, but not a particular form of competition. Competition can be violent or non-violent. It can occur in real-time or by delay.
The following is an example from this old Vanguard post of mine (http://www.vanguardsoh.com/forums/showthread.php?t=5877):
CAPTURE THE FLAG
Guild leaders could arrange the game and invite all guildies who want to play. Members of the competing guilds meet at their guild halls and the guild-leaders invite them to play (/flaginvite); this way, only the guild members who are interested in the temporary PvP are involved. When all members involved are ready and inside their guild hall (if they leave before the start, then they must go back in to be re-invited), the leaders both click start on a pop-up window; it counts down 5 seconds and the fun begins.
Flags appear at whatever point in the guildhalls the leaders specified. Some players might stay behind, but most rush out the door and charge towards their opponents' guildhall to capture the flag. It's PvP, but there are no death penalties other than corpse recovery (which isn't really a penalty, since the game occurs in town). Nobody can be invited into the game once it starts; so if you die, you're out until the game's over. A player who has grabbed a flag is unable to cast or fight. The game will probably (hopefully) end most of the time with very few players left in the competition. Winning rewards the victorious guild with bragging rights and a score kept inside a book in the town library (along with the name of the player who returned the flag), and possibly other fame rewards.
There's a lot of freedom in how that particular game may be played. If the guildhalls are at opposite ends of town, then you might have 5 players of GuildA rushing down mainstreet, while the other 17 or so, who are out to capture the flag, are approaching their enemy through sidestreets and alleys. GuildB might have all 30 offensive players going down mainstreet....crushing GuildA's 5, but failing to keep the other 17 from their flag (emphasizing speed over defense as a strategy). On the other hand, the guildhalls might be right across the street from each other, ensuring utter mayhem every time.
Nobody would be able to attack the players in the game other than other players in the same CTF game. And, like I said, there would be no death penalties. I'm sure some players might be a little sore when they're the 1st person to die, but I think most people would be having tons of fun.
The main concern is player levels. I'm not sure how difficult it would be for a few level 20 players to kill the level 40 player who is guarding the enemy flag (it would depend on the game).
Maybe all players, for the duration of the game, would have their level and stats evened out to the same numbers. Also, the only weapon players can use is a wooden club that magically appears in the hands of all participating players. Then they are all equal and can club each other to death. The guild leaders might even agree on a specific weapon type per match, ala FPS PvP like in Goldeneye or Halo.
Or it might be a lot more fun just to leave all participants exactly how they were before the fight. If one guild has a level 60 player and the other's highest member is level 45, they could just work it out between themselves. And the numbers may even out somewhat once the game's been out a while anyway.
There are, of course, many other possible avenues of PvP in MMOs.
Jousting for a fantasy game. Something like Tron's version of jai lai for a sci-fi game.
Chess or checkers as a way for players to actually enjoy their gameworld homes.
Players could have in-game competitions for best homes or best "paintings" (see that Vanguard post for an explanation).
I seem to remember people telling me alternate PvP systems such as these existed in older MMOs like Ultima Online or Anarchy Online. If so, I applaud those games' developers. But the majority of Western MMOs seem to have followed the example of games like Everquest, which strangely avoided avenues of competition that are not as susceptible to griefing and other common problems of duel-type PvP.