Major spoilers for the Game of Thrones series finale ahead. Deep down, didn't you kind of know something like this would happen? The "winner" of Game of Thrones wasn't an easy answer, fitting as the question was never easy to begin with. Nobody won the Iron Throne on Game of Thrones, because there is no Iron Throne anymore — thanks, Drogon! That chair was pretty ugly to begin with, so maybe it's for the best.
Sure, technically Brandon "the Broken" Stark is the King of Westeros/the Seven Kingdoms at the end of the series. That appears to be temporary, as he can't produce heirs — the council of Lords will presumably choose a new King or Queen when Bran dies. Then again, the last Three-Eyed Raven lived a very long time, so maybe that won't be a concern for a while.
For a hot second, it looked like Westeros was going to go the way of a democracy. Samwell Tarly suggested it at the meeting of the Lords and Ladies that determined both Tyrion Lannister's fate and the fate of the realm. That meeting, by the way, brought back some real "who's who" of Game of Thrones, like Robyn Arryn and Edmure Tully. Even the newly minted Lord Gendry Baratheon was there.
Back to the matter at hand: the rightful ruler of the Throne. If you want to get really technical about it, the last "winner" of the Iron Throne was Daenerys Targaryen herself; she did what she set out to do. Unfortunately, the Iron Throne did to Daenerys what it did to Robert Baratheon, Joffrey, Tommen, Cersei, and pretty much the entire Targaryen line: it corrupted her. The real villain in Game of Thrones was the Throne itself.
By that logic, Bran should be a pretty good King. He even assembled a decent Small Council. Tyrion Lannister is his hand. Ser Brienne is Lord Commander of the King's Guard. Ser Davos Seaworth is Master of Ships, and Bronn of the Blackwater is Master of Coin. Mister "The Prince of Dorne" is in the Dorne position, and Samwell Tarley is Grand Maester. All that's left is Whisperers, War, and Law.
Might I suggest some more women, please — perhaps Meera Reed could fill one of those positions? After the way Bran ditched her in Season 7, he kind of owes her that favor. It's a little odd that Yara Greyjoy was neither Master of Ships nor asking for the Iron Islands to be independent — something they've wanted in the past. Maybe its for the best, as Bran's council was annoyingly low on X chromosomes.
Speaking of independent women, Sansa Stark won a throne at the end of everything. She was crowned Queen of the North and got to reclaim her people's independence, doing the thing her family set out to do in Season 1.
So, as Game of Thrones took its final bow... did everyone win? Did nobody win? It sort of seems like Westeros is going to be OK for a while, and that the surviving characters may actually work together in order to rebuild and maintain peace. Whether or not you like the idea of King Bran the Broken, the Iron Throne pretty much had to go — and everyone in Westeros is definitely better off for it.