Planescape: Torment - You're an amnesic immortal. 
Oh and your (possible) buddies are a floating skull, a thief with demonic blood in her veins, a dude who can shape his sword with his will, a succubus, a burning mage, a living armour and a defective robot...
Broken Sword - Wisecracking patent attorney.
Eternal Darkness - I'm not going to write that all down...
Vagrant story - The reinforcements. 
 
Blood Will Tell: Osamu Tezuka's Dororo - You're pretty much disabled, but you've got some top notch medieval cyborg technology to keep you going. *cough* The game starts in black & white until you get your first eye back, actually.
What's 'usual' in games, anyway? Young townsfolk, soldiers, spies...? 
Game characters' roles are all over the place... It would be truly unusual if the characters' roles would impact the gameplay too.