The Seven Crowns
The sixteen ruling Targaryen kings (and one ruling queen, arguably) of Westeros wore seven crowns between them, as follows:
- Aegon I, Maegor I, Aegon II, Daeron I: a circlet of Valyrian steel embedded with square-cut rubies. Presumed lost or destroyed when Daeron I was cut down and killed during his attempt to retake Dorne.
- Aenys I: an elaborate and gaudy crown of gold. Not worn by any other king.
- Jaehaerys I, Viserys I, Rhaenyra: a simple gold band inset with seven gemstones. After Viserys I's death, the crown passed to his oldest child, his daughter Rhaenyra, but her younger half-brother Aegon II disputed the succession. Rhaenyra was forced to sell her crown at one point to buy passage on a Braavosi ship back to Dragonstone.
- Aegon III, Viserys II, Aegon V: A slender gold band with no ornamentation. This crown was lost in the Great Fire of Summerhall, where Aegon V lost his life and the summer palace of the Targaryens was burned to the ground in an ill-fated attempt to hatch dragon eggs.
- Baelor I: a simple crown of actual flowers and vines. Actually multiple crowns, probably renewed every day or two.
- Maekar I, Jaehaerys II: a crown of black iron and red gold, sharply pointed. This crown's fate is unknown; Jaehaerys II died of natural causes, so the crown was presumably retained in the Red Keep or on Dragonstone.
- Aegon IV, Daeron II, Aerys II: a huge and heavy crown made of red gold, each of its points a dragon's head with gemstone eyes. Worn reluctantly by Daeron II to make a point that he was his father's son, given that rumours of his true parentage dogged his life and triggered the civil war known as the Blackfyre Rebellion. This was also the crown of Aerys II, the Mad King, and fell from his head when Jaime Lannister slew him at the foot of the Iron Throne.
Fate of the Crowns
It should be noted that the ultimate, canonical fate of none of the crowns has been 100% firmly established in the books. However, we can make strong and educated guesses. The first crown was lost in Dorne and, as far as we know, was not returned to the Iron Throne when Dorne joined the realm. Given that Daeron I died in an ambush with a relatively small number of combatants, rather than the chaos of a full-scale battlefield, we can reasonably guess that the crown survived. Whilst it could have been knocked over a ravine or lost in some fashion, most likely it was recovered from the battlefield and secreted away, possibly by a common Dornish soldier but much more likely by a nobleman. The Martells having secured the crown and kept it hidden for generations is quite possible.
The second crown sounds quite hideous and the fact it was never worn against suggests it was probably melted down, broken up, sold or destroyed, possibly on Maegor the Cruel's orders.
The third crown was sold to a Braavosi merchant, so it was likely again broken up, sold on or destroyed for its parts.
The fourth crown's fate is the closest we have to being certain: it was likely utterly destroyed during the burning of Summerhall.
The sixth crown (the fifth doesn't really count, being effectively shrubbery) is the one most likely to have survived intact in the Red Keep or back on Dragonstone. Assuming Robert didn't destroy it, it may simply be on display somewhere, or locked in the treasury, or perhaps "liberated" by Varys for some future royal head?
The seventh crown was the one worn by Aerys II, the Mad King, and it was very likely destroyed by Robert Baratheon, who had a terrible hatred of the Targaryens in general and the Mad King in particular, and would have not let it survive as a symbol for Targaryen loyalists to rally around.
On this basis, both the first crown - the one worn by Aegon the Conqueror himself - and the sixth are likely to have survived in some fashion, and may yet find their way in the possession of a future claimant to the Iron Throne.