These are good pairings for different classes and who they should shoot for when questing or grinding.
Priest: look for rouge, druid, hunter (with dps pet)
druid: goes with just about anything, since a druid is anything. Preferably a high dps class.
warrior: Priest, possibly dps character if the enemies are a few levels weaker.
rouge: war,druid, or priest. paladin is best
shaman: virtually anything
mage: war, war, war. Possibly an experienced priest
hunter: DPS character, but have you pet taunt often.
paladin: since its basically a priest and a war combined, it can go with everything, especially druids, warriors, priests, mages, or best of all, rouges
warlock: Since it has such a wide variety of pets available, it can adapt with any partner. Although a warrior might be best.
Thinking of making a trifecta listing, but that would take a lot longer.