shadow has some terrible, terrible, TERRIBLE advice.
The best solo PvP classes are either Rangers (Qeynos) or Assassins (Freeport). They have the handy combination of Track (find other players to gank, see other people coming for you before they get there and get out of the way), Stealth (harder to see, harder to track), extremely strong burst DPS (drop someone fast then get out of there, even in a group) and Evacuate (.5 second casting time spell that ports you and your group out of the area - basicially a "Get out of jail free" card if you start to lose a fight). Rangers tend to specialized more in ranged damage, assassins more in close-up damage; in general Assassins do have the advantage, but both are superb PvP classes.
Next up would be either Conjurors or Necromancers. While having your tanking pet out is rather... worthless in PvP, in general they tend to be extremely strong when they have their mage pet out in PvP, simply because they can have their pets do good DPS while they do their best to stay out of range, either through just running around or rooting.
Most healers are very strong in terms of PvP, but if I had to pick one it'd either be the Warden or the Fury. Fury's are more offensively oriented, and do occassionaly get very strong nukes; Wardens are more defensive, and they get Evacuate if they get into trouble.
For PvPing as a Fighter, it has to be either Berserker or Brawler (Monk or Bruiser). Crusaders (Paladin/Shadow Knight) tend to be godawful in PvP, and a Guardian is... well, no. Pick either a Berserker (Plate tank, good AE damage especially at higher levels, very good regenerate abilities) or a Brawler (good stuns, high DPS, avoidance tank - tends to dodge most abilities but if they land they hurt) if you want to spend a fair bit of time soloing.