Cloud - Knight (Cover, Hp + etc.)
Vincent - Red Mage (Some Healing and Some Offensive Materia)
Aerith/Cait Sith - White Mage (Healing Materia)
Cid - Dragoon ('Cause of his spear...)
Barret - Either Monk (With Hp+ and Counte, etc.) Or Black Mage (Offensive Magic), depends on the other characters.
Yuffie - Thief/Ninja (Throw and steal materia)
Red XIII - Summoner (Summon Materia)
Tifa - Monk (Hp+, Counter, etc.)

Those are the classes I try to keep my characters as, though sometimes I add Different magic or summons to other characters.