. . . the shape of shadows . . . morrows not yet made . . . drink from the cup of ice . . . drink from the cup of fire . . .

This ties in well with Rhaegar's "song of ice and fire", as well as the overall series title which Martin has indicated as containing several meanings.

. . . mother of dragons . . . child of three . . .
. . . mother of dragons . . . child of storm . . .
. . . mother of dragons . . . daughter of death . . .
. . . mother of dragons, slayer of lies . . .
. . . mother of dragons, bride of fire . . .

"Child of three" is very obscure. In a literal sense, one would have said that she was such a child due to being descended both from Aegon and Rhaenys and Aegon and Visenya. However, she claims her descent to be solely from Aegon and Rhaenys. Another possibility is that just as she is mother to her dragons, they will grow to be her protectors and she will be like a child to them. Yet another possibility is that Daenerys is not in fact Aerys's daughter, but Rhaegar's by an incestuous relationship with his own mother -- however, this is a fringe theory and not one we favor.

"Child of storm" is straightforward, given Daenerys Stormborn, just as "daughter of death" is given her mother's death at her birth and the deaths of Aerys (or Rhaegar, if one prefers such a theory) not long after her conception. On the other hand, it may refer to the turmoil and death her claim to the throne and her role in the war against the Others will bring. "Slayer of lies" may point towards Dany going to Asshai to learn truth as Quaithe suggested to her; see more about Quaithe's prophetic suggestion elsewhere. "Bride of fire" is also clear, given the births of the dragons, her status as the Unburnt, and her role in the "song of ice and fire".

. . . three heads has the dragon . . .
. . . three fires must you light . . . one for life and one for death and one to love . . .
. . . three mounts must you ride . . . one to bed and one to dread and one to love . . .
. . . three treasons will you know . . . once for blood and once for gold and once for love . . .

Again, the three heads is re-iterated before the Undying move into a series of three prophecies concerning threes. It is our opinion that the first one of each of these have already been fulfilled -- the birth of the dragons as the fire lit for life, her marriage to Drogo as the mount ridden to bed, and Mirri Maz Duur as the treason for blood. The destruction of the House of the Undying shortly after this prophecy may fulfill the fire lit for death.

It is far too early to tell what the fire lit for love may be, but many speculate that Dany will fall in love with Jon Snow. The mount ridden to dread almost certainly must be Daenerys taking a dragon to fight the Others, or perhaps simply in a great battle to win her birthright, while (again) the mount to love cannot be decided upon with any hope of certainty. The treason for gold is variously believed to either have been already been fulfilled by Jorah by his sale of information concerning Daenerys to Varys or will be fulfilled by a betrayal from Illyrio Mopatis or the sellsword Daario Naharis. We favor the latter idea, and in particular believe that Daario is the likeliest suspect.

This leaves the treason for love which, with all else, remains a mystery. We do not believe this has been fulfilled, despite occasional arguments that Jorah's betrayals of Dany's trust constitutes a treason for love. On the other hand, of all the prophetic utterances concerning love, the treason for love certainly seems likeliest to be due to Jorah at some point.