Billy grew up foraging in the Wasteland and was eventually hired on to protect caravans. Life was nothing but profit and survival until he came across Maggie. After killing the raiders who had massacred Maggie's parents, he took her under his wing. He brought Maggie to Megaton and helped fend off a Raider attack. He was given the house of a settler who was shot in the attack. There are a few around town who say that Billy was the one behind the bullet that bought him his place in Megaton.
Colin Moriarty, on the other hand, has his own thoughts on Billy Creel. According to what can be found on his terminal, he suspects Billy Creel killed Maggie's parents himself, and kept the girl as a "trophy". However, this is probably false, given that Billy drops an ear when killed (as good characters do) rather than a finger (that evil characters drop). A more logical explanation is that Colin, being inherently greedy and selfish himself, cannot understand a selfless act like adopting an orphaned child. Moriarty also describes him as a "Nuka-cola swilling prick", which suggests that Billy doesn't drink alcohol.
Billy doesn't have any known biological family, but he considers Maggie to be his own daughter, after rescuing her from raiders. He doesn't have any enemies, but Colin Moriarty is not very fond of him.
If the Lone Wanderer maintains a good Karma level, Billy is quite friendly with him/her.