Rarely. I have only tried one same character concept - Thordek Lightbringer, a dwarven character - in multiple CRPGs, and even then, they varied a lot in between. In the Baldur's Gate saga, he was a Barbarian, IIRC; in NWN, he was a Fighter/Cleric, then a Fighter, then a Paladin; in Temple of Elemental Evil, he was a Fighter/Cleric, then a Paladin; in Arcanum, he was a fighter-type who wielded a pyrotechnic axe and a flamethrower.
All other characters are wildly different between themselves and between games.