Any class can effectively solo, they just do it differently.
As a fighter, your DPS will be relatively low and defense will be high resulting in longer fights. Guardian has the highest defense.
Healers are also low on DPS but they can heal themselves through a fight. Shaman's have effective debuffs, Wardens have many buffs.
Scouts have a high DPS and can either attack ranged (Ranger is best) or melee from behind (Assassin is best). Other scout classes have good DPS. Troubador/Dirge have less DPS but more buff songs.
Mages are on the top of DPS; Conjurers (good vs groups) and Necromancers (good versus solo) have the pet to help them keep the fight at arms length.
Wizards/Warlocks are at the top of the food chain for DPS, with a level 50 DD spell that does 4K damage. They use roots, stuns, and mezs to keep the mob away - bad news if it breaks though.
As a Conjurer I can take on many mobs at once with the pet keeping agro while I cast DD and DoT's. I can take a group of 5 yellow^, or one blue^^^.