It is actually possible that Jaime and Cersei and/or Tyrion are Targaryen bastards born of the Mad King and Joanna (their mother) through rape. Apparently Aerys had quite the fancy for her, and he was known for taking what he wanted. It helps to explain (beyond even him being a dwarf) why Tyrion gets so much bile from his father if he is either A. The bastard of the man who raped his wife, or B. His one and only trueborn child.
I thought this was total crackpot until I got to A Dance with Dragons and Barristan specifically discusses Aerys and Joanna and is stopped before he can go any further with the tale. Didn't convince me, but made me suspicious.
Personally I hope it isn't true as too many "Actually, he's a Targ!" revelations in the final book could be redundant, but if it is true that Aerys and Joanna produced a bastard, I'd prefer it be Jaime/Cersei for the symmetry that both Tyrion and Jaime murdered their own fathers.