I am going to start with the Starks.
The romance that I possibly like best in the entire series is Robert and Talisa Stark. A strong contender would be Ygritte and Jon Knower-of-nothing Snow but I'll come to that later. The two above-mentioned women are also my top favorite female characters. But alas, the Robert/Talisa romance which is perfect it is also short-lived. The beautiful couple is killed at the Red Wedding.
Next comes Sansa who, as we know, is arguably the character that has grown most over the 8 seasons. The adolescent girl's fantasy about romance is quickly and brutally annihilated. Towards the end, I actually hoped that Sansa and Tyrion will consummate their marriage and jointly rule the Seven Kingdoms. But that is not to be.
There was one brief moment when something may blossom between Bran Stark and Meera Reed. With the trajectory that is Bran's "story" (courtesy Tyrion) was taking, however, this is understandably nib in the bud.
In terms of basic personality Arya has not really changed as much as her sister. Arya just expanded. I do like her connecting with Gendry and there are advocates that they should jointly rule the Seven Kingdoms. But the romance, after all, is not totally convincing. More like a passing infatuation, when it seems that that world was going to end.
I think I'll include Jon Snow under the Starks. Frankly, I don't find the romance between Jon and Dany convincing. More like a plot device. I am sure that there are at least some who would agree with me that the romance between Jon and Ygritte is among the most touching in the series. It is not unlike a fateful Romeo and Juliette love affair (except that here we have an Amazon of a Juliette).
So, not happy endings in Stark romances. Let's move on to the Lannister.
Jamie and Brienne, after starting out on a rocky road, wound up having everybody rooting for them. Indeed, they are the nearest to being soulmates, not the least because of they both rank among the top fighters in Westeros. Those who remember may recall that the Flower Knight bested Jamie, and later Brienne beat the Flower Knight, even before we know the face behind the helmet belong to someone call Lady Brienne. Given that those two battles were tournaments and not real fighting, that still means something. It is sad to see that his destiny was not to spend the rest of his life growing old with her.
Tyrion, I mentioned in conjunction with Sansa, married but entirely unromantic. They do make a very good pair though and should be the best choice to rule the Seven Kingdoms. They each did quite well though, as queen of the independent north and hand of the king of the Six Kingdoms. Happy endings, although separately.
On the Baratheon, I mentioned Gendry in conjunction with Arya. Renly, probably the best of them, would make a best- looking pair with Margaery Tyrell, even when that was only for shows as he loved her brother instead, the Flower Knight. In any event he was murdered by witchcraft, starting Margaery's career as a professional Baratheon widow. From her second husband hideous monster Joffrey she was saved by angelic grandma Lady Olenna, the Queen of Thorns, via poisoning him. The third husband Tommen was a darling of a boy king, who did not make her a widow but instead killed himself after she died in his mother's hands, sort of a poetic justice revenge "You kill someone I love, and now I kill someone you love".
Is there any romance that ended happily? The obvious one is Sam and Gilly. And they were even blessed with their own offspring eventually. It was such sublime joy to watch how Sam, embarrassingly and apologetically, explained to Jon the reason why Gilly was pregnant was because after reading all the books, he still had plenty of time and nothing much to do in the Citadel.
Finally, I must mention one relationship that is so unique that defies description. Certainly not romance. He was on her to-kill list. She was his bounty-hunter's prize for a handsome ransom. Situations evolved. When they met again in the final season, he said "The last time we met, you left me to die". Her reply: "First, I robbed you". In the end, they were travel companions for one last time, both seeking death. In the very end, when The Hound went to meet his destiny at the "Clegane Bowl" he accomplished on final good deed: success in convincing Arya that she needed not, and should not die. Her parting three words to him "Sandor. (pause) Thank you" is the nearing thing in the entire 8 seasons to bringing me to tears.