Raul, ED-E and Rex.
Raul and ED-E deserve their own books or movies (who wouldn't watch a movie about Raul's life?). They both just seem like oddities at first, but once you dig into their pasts, they turn out to have two of the most detailed and interesting backgrounds in the series.
Rex because unlike the others, he can't outright tell you his story. He's obviously got an interesting story to tell just from seeing his surroundings. He's an Elvis impersonator's Cyber Dog who was obviously bred for combat and has a Legion emblem on his side. You don't get any real answers during his questline about his origins. That makes me interested in finding them myself. It takes a bit of searching to actually find someone capable of telling you Rex's background.