Episode 4 spoilers within!
Daenerys Targaryen started as something of an unlikely contender for the Iron Throne of Westeros in Game of Thrones--the displaced princess was alone with her brother on another continent, with few supporters, no armies, and spies and assassins sent by Westeros' then-king, Robert Baratheon, hounding them. But since the end of the first season, Dany has had a major military advantage no one could match: dragons. She used them to liberate cities and free slaves across Essos before finally returning to Westeros to fight the Lannisters and the army of the dead. Dragons are so powerful, they ushered in the 300 years of Targaryen rule in Westeros before Daenerys was born.
Having air superiority has made Daenerys nearly unbeatable in recent seasons, but she lost one of her dragons in the war against the Night King and the White Walkers. That left her with only two.
Qyburn, Cersei Lannister's Hand of the Queen, also developed a weapon that could take down dragons, giving Cersei a chance to fight back against the otherwise unbeatable creatures. The giant crossbow, known as a scorpion, can knock dragons out of the air--and in Episode 4, "The Last of the Starks," Euron Greyjoy and the Iron Fleet manage to use them, mounted on their ships, to kill Rhaegal, the dragon Jon Snow rode in the Battle of Winterfell. That means Daenerys just has Drogon, her largest and most fearsome dragon, remaining.
But is that really it? Dragons have been a game-changer in the world, which raises an additional question: Could there be more?
Up until Dany's three dragons were born, it was common knowledge the world over that the species had gone extinct. But there are potentially more dragon eggs out in the world, left behind by the Targaryens at various points in history. If Daenerys's eggs were formerly stones (or appeared to be stones), those others could potentially still be viable as well.
In George R.R. Martin's "A Song of Ice and Fire" books, on which Game of Thrones is based, there are a number of dragon eggs mentioned at various points. Targaryens used to give their young princes dragon eggs even as infants, to try to get the dragons to bond with them as early as possible. But not all of those dragon eggs hatched, and at various times, Targaryens took eggs with them to different places, like the Vale--and we don't know what happened to them all. There's also a mention in the companion book "The World of Ice & Fire: The Untold History of Westeros and the Game of Thrones" of a rumor that a Targaryen dragon laid eggs in the Winterfell crypts almost two centuries before the events of the show, near the hot springs there. So there are at least a few dragon eggs supposedly lost and scattered throughout Westeros.
There's also a theory that Daenerys has more dragons than even she knows about. Remember when Drogon was missing for most of the fourth and fifth seasons, when Dany had her other two dragons chained beneath the great pyramid in Meereen? There's speculation Drogon might have flown off to go lay some eggs. Dragon reproduction gets discussed a bit in the books, including the idea one maester puts forward that they can change sex between male or female in response to their reproductive needs. Like everything to do with them, though, dragon reproduction is barely understood in Martin's world--so the possibility is definitely there in Game of Thrones.
The interesting thing is that the return of dragons has had larger effects on the Game of Thrones world than their incredible power and military superiority. There's a big implication in both the books and the show that the return of dragons has also meant the return of magic to the world. We saw as much in Qarth in Season 2, when Daenerys dealt with the sorcerers there, and there's speculation that the time was right for White Walkers to make their push against the realms of men after centuries of no one having heard from them at all because of the rebirth of dragons. So while it's a bit speculative, it does seem possible that while Daenerys has lost two of her three dragons, they won't necessarily be the last.
For the time being, though, there's just one for sure dragon left in the world, and that's Drogon, since Viserion was killed by the Night King, turned into a wight, and killed again when Arya destroyed the White Walkers, and Rhaegal is now apparently at the bottom of the sea with a scorpion bolt in his neck. Dragons changed the world of Westeros once before, and while Daenerys's dragons haven't had the same effect that Aegon the Conquerer did when he took over Westeros and started the Targaryen dynasty 300 years before the events of the show, it still seems possible that they could change it again in the future.