Just for fun, I've made a list of the references to the "three heads of the dragon" excluding descriptions of the Targaryen family sigil as represented on banners/Rhaegar's breastplate, etc.
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And the Tourmaline Brotherhood pressed on [Dany] a crown wrought in the shape of a three-headed dragon; the coils were yellow gold, the wings silver, the heads carved from jade, ivory, and onyx.
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Viserys, was her first thought the next time she paused, but a second glance told her otherwise. The man had her brother’s hair, but he was taller, and his eyes were a dark indigo rather than lilac. “Aegon,” he said to a woman nursing a newborn babe in a great wooden bed. “What better name for a king?”
“Will you make a song for him?” the woman asked.
“He has a song,” the man replied. “He is the prince that was promised, and his is the song of ice and fire.” He looked up when he said it and his eyes met Dany’s, and it seemed as if he saw her standing there beyond the door. “There must be one more,” he said, though whether he was speaking to her or the woman in the bed she could not say. “The dragon has three heads.” He went to the window seat, picked up a harp, and ran his fingers lightly over its silvery strings. Sweet sadness filled the room as man and wife and babe faded like the morning mist, only the music lingering behind to speed her on her way.
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“I have come for the gift of truth,” Dany said. “In the long hall, the things I saw . . . were they true visions, or lies? Past things, or things to come? What did they mean?”
…the shape of shadows . . . morrows not yet made . . . drink from the cup of ice . . . drink from the cup of fire . . . mother of dragons . . . child of three . . .
‘Three?” She did not understand.
… three heads has the dragon . . . the ghost chorus yammered inside her skull with never a lip moving, never a breath stirring the still blue air. . . . mother of dragons . . . child of storm . . . The whispers became a swirling song. . . . three fires must you light . . . one for life and one for death and one to love . . . Her own heart was beating in unison to the one that floated before her, blue and corrupt . . . three mounts must you ride . . . one to bed and one to dread and one to love . . . The voices were growing louder, she realized, and it seemed her heart was slowing, and even her breath. . . . three treasons will you know . . . once for blood and once for gold and once for love . . .
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“The dragon has three heads,” she sighed. “Do you know what that means, Jorah?”
“Your Grace? The sigil of House Targaryen is a three-headed dragon, red on black.”
“I know that. But there are no three-headed dragons.”
“The three heads were Aegon and his sisters.”
“Visenya and Rhaenys,” she recalled. “I am descended from Aegon and Rhaenys through their son Aenys and their grandson Jaehaerys.”
“Blue lips speak only lies, isn’t that what Xaro told you? Why do you care what the warlocks whispered? All they wanted was to suck the life from you, you know that now.”
“Perhaps,” she said reluctantly. “Yet the things I saw-”
“A dead man in the prow of a ship, a blue rose, a banquet of blood . . . what does any of it mean, Khaleesi? A mummer’s dragon, you said. What is a mummer’s dragon, pray?”
“A cloth dragon on poles,” Dany explained. “Mummers use them in their follies, to give the heroes something to fight.”
Ser Jorah frowned.
Dany could not let it go. “His is the song of ice and fire, my brother said. I’m certain it was my brother. Not Viserys, Rhaegar. He had a harp with silver strings.”
Ser Jorah’s frown deepened until his eyebrows came together. “Prince Rhaegar played such a harp,” he conceded. “You saw him?”
She nodded. “There was a woman in a bed with a babe at her breast. My brother said the babe was the prince that was promised and told her to name him Aegon.”
“Prince Aegon was Rhaegar’s heir by Elia of Dorne,” Ser Jorah said. “But if he was this prince that was promised, the promise was broken along with his skull when the Lannisters dashed his head against a wall.”
“I remember,” Dany said sadly. “They murdered Rhaegar’s daughter as well, the little princess. Rhaenys, she was named, like Aegon’s sister. There was no Visenya, but he said the dragon has three heads. What is the song of ice and fire?”
“It’s no song I’ve ever heard.”
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“Belwas has the truth of us, Your Grace,” said Arstan. “We were told to find you and bring you back to Pentos. The Seven Kingdoms have need of you. Robert the Usurper is dead, and the realm bleeds. When we set sail from Pentos there were four kings in the land, and no justice to be had.”
Joy bloomed in her heart, but Dany kept it from her face. “I have three dragons,” she said, “and more than a hundred in my khalasar, with all their goods and horses.”
“It is no matter,” boomed Belwas. “We take all. The fat man hires three ships for his little silverhair queen.”
“It is so, Your Grace,” Arstan Whitebeard said. “The great cog Saduleon is berthed at the end of the quay, and the galleys Summer Sun and foso’s Prank are anchored beyond the breakwater.”
Three heads has the dragon, Dany thought, wondering. “I shall tell my people to make ready to depart at once. But the ships that bring me home must bear different names.”
“As you wish,” said Arstan. “What names would you prefer?”
“Vhagar, “ Daenerys told him. “Meraxes. And Balerion. Paint the names on their hulls in golden letters three feet high, Arstan. I want every man who sees them to know the dragons are returned.”
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“My queen,” [Jorah] said, “and the bravest, sweetest, and most beautiful woman I have ever seen. Daenerys -
“Your Grace!”
“Your Grace,” he conceded, “the dragon has three heads, remember? You have wondered at that, ever since you heard it from the warlocks in the House of Dust. Well, here’s your meaning: Balerion, Meraxes, and Vhagar, ridden by Aegon, Rhaenys, and Visenya. The three-headed dragon of House Targaryen - three dragons, and three riders.”
“Yes,” said Dany, “but my brothers are dead.”
“Rhaenys and Visenya were Aegon’s wives as well as his sisters. You have no brothers, but you can take husbands. And I tell you truly, Daenerys, there is no man in all the world who will ever be half so true to you as me.”
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“No doubt he will,” said Lord Tywin. “All the same, you must be crowned at the king’s wedding. Cersei, summon your goldsmiths, we must see to a replacement.” He did not wait for her reply, but turned at once to Varys. “You have reports?”
The eunuch drew a parchment from his sleeve. “A kraken has been seen off the Fingers.” He giggled. “Not a Greyjoy, mind you, a true kraken. It attacked an Ibbenese whaler and pulled it under. There is fighting on the Stepstones, and a new war between Tyrosh and Lys seems likely. Both hope to win Myr as ally. Sailors back from the jade Sea report that a three-headed dragon has hatched in Qarth, and is the wonder of that city - “
“Dragons and krakens do not interest me, regardless of the number of their heads,” said Lord Tywin. “Have your whisperers perchance found some trace of my brother’s son?”
Dany definitely seems vested in three dragons for three heads of the dragon, and the number three is often related to her in a number of different ways. She's called the child of three, and her visions in later part of the House of the Undying are delivered in three groups of three.
Edited by Sevumar, 05 February 2012 - 08:33 PM.
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let me tell you that you're freaking good with theories. I like this one, cause I really dislike that "3 heads 3 riders" theory. I had myself a theory (yes, a bit absurd) about the 3 heads being the dragon itself, the rider and a warg ("warging" the dragon, obviously 
) but yours, makes much more sense since I'm pretty convinced that when a prophecy talks about dragons means Targs and not real dragons.So, Jon: Snow, Stark and Targaryen, a dragon with 3 "heads" just saying 
