The Character: Little Kal-El, the Last Son of Krypton, lands in Gotham City instead of Smallville. Found by the wealthy Wayne family, they adopt him and name him Bruce (they don't have a biological son in this scenario). Then, as one day they head home from the cinema, a thug shoots Thomas and Martha Wayne dead. That's when little Bruce realizes he has superpowers...by killing the thug with his Heat Vision. Enraged, he dons the Batsuit when he grows up and starts his crusade against crime.
You can't be rich AND have superpowers. You only get one!
The Game That Could Be: DC's two finest, in one character. Batman's resolve and genius intellect and Superman's godlike powers. It would be a really interesting concept, for one reason. While we love Batman for holding his own next to metahumans with no superpowers, one of the great things about gaming is empowerment. In the games, we can slay dragons, fight gods and master The Force. Playing as an empowered Batman would be like a playground. The greatest villains of Batman and Superman - with Lex Luthor as The Joker, mind you - and most of the game would still be about being a god among insects. Guys like Darkseid and Metallo and some kryptonite could keep the difficulty in check to ensure one hell of a playing session.
The Character: The classic Batman origin story, with one little twist. Instead of being the lone survivor, little Bruce Wayne is the only casualty on that fateful night. Thomas Wayne overpowers and beats the thug, and decides to wage war on crime for losing his son, becoming the Batman. His wife, Martha loses her sanity due to the sudden loss of her child, becoming the homicidal maniac Joker.
Well, at least he'll never grow up to become Ben Affleck.
The Game That Could Be: An older, meaner Batman with slower, but more devastating attacks could shake up the standard Arkham playing style a bit. Also, Batdad doesn't have Junior's no-kill policy, freely using lethal attacks and even guns in his fights. Ironically, despite him being more violent than the Bruce Wayne version, this Batman has a compelling reason to NOT kill The Joker. She is, after all, his wife and the last person he can call family. It would be Batman meets Snake Eater, with the protagonist having to fight the most important woman in his life. The plot has everything one could wish from a well-written, touching and memorable AAA title. Where is Paul Dini when you need him? The man should have his own Bat-Signal.