Official Word of God says:
Lastly, some fans are reading too much into the scene in GAME OF THRONES where the dragons are born -- which is to say, it was never the case that all Targaryens are immune to all fire at all times.
Source: The Citadel: So Spake Martin - Egg and the Targaryens
Also this (sourced from A question about Daenerys Targaryen in a Song of Ice and Fire (spoilers) - Forum - DakkaDakka):
Granny: Do Targaryens become immune to fire once they "bond" to their dragons?
George RR Martin: Granny, thanks for asking that. It gives me a chance to clear up a common misconception. TARGARYENS ARE NOT IMMUNE TO FIRE! The birth of Dany's dragons was unique, magical, wonderous, a miracle. She is called The Unburnt because she walked into the flames and lived. But her brother sure as hell wasn't immune to that molten gold.
Revanshe: So she won't be able to do it again?
George RR Martin: Probably not.
