viz, my idea is not even a theory, there is not one shred of evidence to back it up. Because of this, no one can disprove it either!
Basically, Aerys the mad king raped Joanna while Tywin was off on a business trip. Joanna knowing that Tywin would never allow such an affront to go unchallenged decided no to tell Tywin because House Lannister would have been obliterated in a confrontation with the throne. Joanna died in childbirth or the complications thereof and, Jaime slew Aerys, and the Kingsguard are all dead and so the secret has been buried, except for Barristan and Varys.
It's pure speculation, but here's what makes me think it's true. 1) Aerys raped his own wife. When Jaime started to protest to the White Bull, Hightower shut him down by saying that teh Kingsguard never stopped the king from anything. 2) Tywin told Tyrion that he doubted if he were his son. 3) The myth in Westeros is that bastards are malformed and grotesque. 4) Tyrion told Jon that all dwarves are bastards in their father's eyes. 5) Tyrion is fascinated with drgons. 6) Tyrion defended KL with House Targaryen's own champion... fire. 7) Maester Aemon called Tyrion a giant among men. 8) Tyrion and Jon became good friends, not as Stark and Lannister, but because both are Targ bastards. 9) Dany will need two other Targaryens to help her rule. Aegon is a possibility if he's alive. But like Dany, Jon and Tyrion have experience leading and ruling. 10) I wish it to be true.
Though I do confess that Genna told Jaime tha Tyrion, because of his mannerisms and brains, is Tywin's true son.
Lubbock, why did you say that Tyrion may be a Targ *******? I'd love to hear different reasons than my own.
After sufficiently hijacking Marv's thread, I'll try to respond correctly...
Rhaegar was a stand up guy for the most part. But one stupid mistake collapsed a kingdom.
Sounds like Eddard.
If you don't mind a theory that might be a spoiler, then highlight the rest of the text.
Many posters think that Rhaegar and Lyanna eloped or at the least that Lyanna willingly went with Rhaegar to bear his child. Meera's stories lend credibility to this.