Long-lasting Fights
In order for a fight to be enjoyable and player skill taken into consideration, it must last. In Ultima Online and Shadowbane, combat between individuals could last long minutes. In Vanguard and World of Warcraft, combat could be over in seconds. The enjoyment is in the fight and the longer it lasts the better.
Quick XP curve and/or XP via PvP.
PvPers want to pvp and not grind mobs endlessly. Allowing for a quick XP curve will allow pvpers to be "ready" sooner. Another benefit is that there won't be as many low level newbies around to be fodder and quit; when players quit of course there are less of them around to pvp with. A fast XP curve means you can get your friends and guildies involved in the pvp faster. Finally, being able to gain XP via pvp is the best of both worlds. The player gets to fight other players and advance through it.
Powerlevel Friends
A major component of a vibrant pvp world is having people to pvp with; the more the merrier. To that end, being able to powerlevel friends and guildies so they "keep up with the Joneses" is key. It's easy to disenfranchise players when you are battling it out in epic combats while they are still killing rats for wheels of cheese. Shadowbane did this very well. A max level character could level 9 afk friends and get them levels in short order.
No Radar
The ability to see people as a blip on the radar is anti-competitive. One should have to use their own eyes to find people in the geometry. This adds tactics, perception becomes important and adds another dimension to the game.
Balance
While we don't expect every single class to be 100% balanced vs every other class, everyone expects to have a chance when they mix it up. There are certain games where one class has absolutely no chance vs another and that is anti-competitive and not fun. PvPers want a chance to win, that's an ingredient of fun.
Many Combat Options to Use While Fighting
In order for a pvper to showcase skill, both he and his target need to have many options and tactics available to them. This allows for skill to really be a factor. If one's only option is to spam the 1 key to power attack over and over then that isn't skill.
Guild Options Such as Tabards
Guilds are proud of whom they are and fighting with your "colors" against enemies with their "colors" adds to the fun of combat.
Death Penalty and Looting
The system in World of Warcraft of bind-rushing, no loss, no penalty death is an anathema to true pvpers. It's really a sad symptom of where our society is heading where "everyone's a winner", a bruised ego is seen as an evil rather than a learning experience and you can sue McDonalds for being fat. But I digress. If you and I engage in combat, the loser needs to lose something. Good examples are the vitae system in Asheron's Call, looting in Ultima Online and resurrection sickness. If I kill you, I should not see you again at full health in 10 seconds. Please note the inherent danger in a system that is too harsh is that players will quit and then you won't have anyone to pvp against. Shadowbane is a perfect example of this. Destroy someone's city and half of its players quit making Shadowbane servers ghost towns. UO's "full loot" system worked because items were not very important.
Inter-Server Combat
Become the best on your server? Now prove yourself against those on other servers.
Exploiters Banned
This is self-explanatory. Fun and meaningful pvp can only stem from it being cheat-free. Also, make it public. "Today, Ebonlore was banned for."
Meaningful
PvP should be meaningful. PvP has higher stakes and therefore is more fun if the combat is over something. In Shadowbane many times it was combat for your entire city, in Ultima Online it was your equipment and in DAoC it was your keep and relics.
Buffs and Equipment Not All-powerful
A pvper wants his skill and tactics to be the deciding factor in combat, not buffs and instance-farmed equipment. If my strength is 100, a buff should only give me 10 points or so making it handy but not an all-important necessity. It's also silly that one has to spend 50 hours inside a Molten Core instance pve'ing to get equipment to compete in pvp.
Levels Unimportant
A level should give a small boost but not be a key component when they are similar. For example, a level 40 should have a chance to win vs a level 50. A level 30 should have a chance to defeat a level 38. I am not advocating a 50/50 chance necessarily, but it needs to be greater than 0%.
1 Character per Server
Players can only do "bad" things with more than 1 character. They can make mules to carry loot, mules to grief folks, reroll a toon to lose their earned reputation and use a throwaway scout. For pvp to be meaningful, characters need to keep the reputation they earn. Alternately, if more than 1 character is allowed per server, give all the toons common last names. For example, if your first character's last name is "Johnson" then they all share that name.
Large Server Population
The more people playing, the better the pvp. A player won't have to waste time running all over looking for it and there will be more fights.
Quick Recognition of Enemies
There should be an in-game system whereby you can recognize your enemies. If the server is free-for-all then a guildmaster should be able to mark individuals and guilds as KOS and have their color change.
Virtually no Safe-Zones or Instances
Other than a starter newbie zone, pvpers want to be free to take the fight to their enemies anywhere in the game whenever they can. Instances only turn the combat from a true war where victory is determined by tenacity and will as much as skill to cute little sparring matches that don't prove true warrior spirit.
Ability to Respec or Retrain Abilities
All games go through rebalancing, patches and class changes. Being able to retain our pvp skills allows us to adjust and keep current with these changes without having to reroll another character and grind more XP.
Don't Show Levels
A true PvPer doesn't pick on someone just because they will instantly win, they enjoy fighting and learning other's reputations for those combats. Knowing someone's level doesn't provide any positive benefits.
Ability to Spar and Battle Guildmates
It's a small thing, but the ability to fight friends w/o any penalty or loss makes for fun. Ability to practice, have tournaments or just mess around when things are slow can make for some fun times.
In-game Proof of Victory
Ever read a public forum? Steve says he owned Frank and the next post is Frank saying he owned Steve. An in-game system for proving victory is necessary. In DAoC it was hard to say "PRX Sucks!" with much credibility when our realm had all 6 relics and we were #1 in realm points. In Shadowbane it's hard to say "We pwned you" when your city is a burning hulk and ours is safe and sound and the world map clearly shows you had a larger population than we do. In Guildwars anyone can clearly see how many matches a guild won and how many a guild lost. PvPers want to see hard data on the pvp happening in game.