What happened to all Targaryen's Dragon Eggs?

Question

In the Dunk and Egg novella The Mystery Knight, Dragon Eggs are featured prominently: one of them is the prize of the Whitewalls Tourney hosted by Lord Butterwell, and Egg himself states that he (and his brothers too) also possesses one of them, that was put in his cradle when he was a child.
At the end of the story

we learn that the Targaryens, via Bloodraven, acquire also Lord Butterwell's Egg.

If all the children of a cadet Prince of the Royal Family all possess a Dragon Egg, I think that we could safely assume that they are (relatively, of course) common, or at least not so rare.

We know that seven of them

were probably destroyed during the Tragedy at Summerhall

but what happened to the other ones?

Answer 1

As summarized on the ASOIAF wiki there up to 33 known dragon eggs. We know there was 25 dragons to have lived in Westeros after the Targaryens landed at Dragonstone.

So indeed, in Westeros they were quite rare. However, since it was the monarchs who owned them (not to mention how awe inspiring a dragon is) the histories and lore are filled with their tales!

In Essos and Sothoryos dragons were known to live on almost every part of the continents with various accounts of their origins. So there may be an untold number of eggs waiting to be discovered, such as the eggs given to Daenerys were.

• Mysaria's egg - When Prince Daemon Targaryen learned his concubine was pregnant, he presented her with a dragon egg, but King Viserys I Targaryen commanded him to return the egg and send Mysaria away. Whereabouts unknown.
• {hatched} Prince Jacaerys Velaryon's egg - placed in his cradle at his birth by royal decree, hatched into the dragon Vermax.
• {hatched} Prince Lucerys Velaryon's egg - placed in his cradle at his birth by royal decree, hatched into the dragon Arrax.
• {hatched} Prince Joffrey Velaryon's egg - placed in his cradle at his birth by royal decree, hatched into the dragon Tyraxes.
• King Viserys II Targaryen's egg - he possessed an egg during the civil war of the Dance of the Dragons, so far undescribed – whereabouts unknown.
• Lady Rhaena Targaryen's eggs - her first egg hatched into a broken thing that died within hours. She possessed another egg at the start of the civil war, and took three eggs to the Vale with her during the war. Only one egg is known to have hatched, the whereabouts of the others are unknown.
• Prince Maelor Targaryen's egg - he was given an egg at birth, which had not yet hatched by the start of the civil war. It is unknown what happened to the egg after Maelor was killed at Bitterbridge.
• Five eggs - from the last dragon's clutch, so far undescribed – whereabouts unknown.
• Princess Elaena Targaryen's egg - silver and gold in unknown arrangement – whereabouts unknown.
• Prince Daeron Targaryen's egg - known to exist, but so far undescribed – whereabouts unknown.
• Prince Aerion Targaryen's egg - gold and silver, with veins of fiery colors – whereabouts unknown.
• Prince Aemon Targaryen's egg - known to exist, but so far undescribed – whereabouts unknown.
• King Aegon V Targaryen's egg - white and green swirls – whereabouts unknown.
• Lord Ambrose Butterwell's egg - red, with golden flecks and black whorls – whereabouts unknown.
• Seven eggs - used by King Aegon V Targaryen in the ceremony that caused the Tragedy at Summerhall. Some of these may have been the unhatched eggs mentioned above. Whereabouts unknown, but possibly destroyed by the fire.
• King Euron Greyjoy's egg - Euron claimed he had a dragon egg, but threw it into the sea.
• {hatched} Drogon's egg - black as the midnight sea, alive with scarlet ripples and swirls.
• {hatched} Rhaegal's egg - deep green, with burnished bronze flecks.
• {hatched} Viserion's egg - colored pale cream, streaked with gold.