As the others said, think of something unique without thinking about the rules at all. Maybe a constantly swaying pirate captain without a ship. Wait a minute...
As for rare race/class combos:
Gray (OMG, the computer didn't type the r at first) or gold (depending on your world) elf barbarian. Should be one of a kind. Coming up with a decent background about how that guy became a raving maimer should make him unique in the sense you meant, too.
Or play a paladin with high dex and int, low str and con. People are accustomed to the big, tough, clumsy, stupid pals. Would work well with races that don't have paladins as is: elves, orcs.
Then, there are bards, but not the usual minstrels. Make a bard who doesn't sing and play the harf/lute. In a novel by Elaine Cunningham, there was a dwarven lass who was very quick with the pen - she painted caricatures, and they usually hit the mark.