I guess I'm in the minority, because I liked it. I just don't think it approaches the terribleness that was the Dexter series Finale. Taking a look at IMDB, the GoT Finale is rated as bad as the Dexter finale. Comon.... A few observations, I read all the replies in here and some of this have already been said, oh well. lol.
Ser Brienne: I feel like once the threat to the realms of men and to the Starks were over, she had fulfilled her oath to Sansa and Arya, who are now, both adults. Arya is a skilled assassin, Sansa Queen of the North. They don't need Brienne's protection anymore and besides, she can't protect them both at the same time. She is originally from the south, so it makes sense that she could become part of the kingsguard. Not to mention the new King is a Stark, so maybe on the other hand, she can continue to fulfil her oath? When Cersei became Queen didn't she choose her Queensguard as well? (Though eventually all she needed was The Mountain). So I had no issue with this, though I'm not sure she really had a vote as the Island of Tarth was part of the Stormlands and thus serving Gendry as the new Lord of the Stormlands. Also, Sansa and Arya know Brienne, I have no doubt they told her stay to serve Bran.
Drogon not killing Jon: Drogon didn't see John kill Dany, Jon has Targaryen blood and Drogon figured he was a friend. I laughed when Drogon destroyed the throne, kinda felt like Drogon was saying, enough of this throne business, Mom was gonna break the wheel, so I melted the throne, good luck silly humans, I'm done with this stupidity <mic drop>. It was sad seeing Drogon nudge Dany, no different than a loyal dog, sad when their human dies.
Bronn: A Lannister always pays his debts. Tyrion kept his word, throughout this whole story he has Kept his word. High Garden provides a lot of the food for the 7 Kingdoms, it makes sense to let him be master of coin. (at least of any of the characters that are left). Also as secondary, the round table at the end I didn't have a problem with. Bronn and Tyrion together were always knuckleheads. I also saw it as a way to lighten the mood. Politics are just so serious sometimes.
Grey Worm not killing Jon: I agree with others that he's used to taking orders. He broke from that when he decided to kill the surrendering Lannister forces in s08E5, however, once his Queen and Drogon were gone, I don't think there was much keeping the Unsullied and Dothraki together. Dany was that glue. Had he killed Jon it would just continue the war and bloodshed. You know the Northman and Sansa would not have stood idle. Also, I think Grey Worm, as we saw at the end, wanted to honor his promise with Missandei by going to Naath. I think he was tired of the bloodshed and had he killed Jon there was no chance of that happening. With Dany now gone, he could do that. Had Dany lived, he be spending the rest of his life "liberating" the rest of Westeros and the Seven Kingdoms. Who knows if he would survive.
Jon going back to Night's Watch: I think everyone involved (except Grey Worm) knew that Jon wasn't going to stay at the Wall. I think Grey worm accepted this because of what I mentioned above. We got our much deserved reunion with Ghost, making up for the departure after the Battle of Winterfell. Jon gets to go back to North of the wall where I think he truly wanted to be. I actually compare this to Grey Worm going to Naath, though he hadn't been there before, it's where Missandei was from. Jon met his first true love North of the Wall (Ygritte) and he was returning there. It's the only place he truly felt where he belonged. As he continually said, he never wanted the throne and I think north of the wall is the only place where he wouldn't be constantly reminded that he was the last true heir to the throne and/or treated as such. The Wildings don't care about that and neither did Jon.
Happy Ending: I keep hearing everyone say this was your typical Hollywood happy ending. I don't see it as that at all. Jon had to kill his Aunt, his second love, until he found out Dany was his Aunt. To save the realm of men. I don't know about you, but I wouldn't consider having to kill a family member a Happy Ending. Drogon lost his mom, not happy. The only living Starks, who were separated for much of this series, end the series separated again. Yes, they may be alive, but they are unlikely to see each other ever again. Sansa, Queen in the North, Bran the Broken, King of the 6 Kingdoms. Arya, going on a walk-about (or sail-about) and Jon back North of the Wall. I don't see where not being able to be with family you love as a Happy Ending.
Finally, this series started with the Starks and it ended with the Starks and I'm not sure it could have ended any other way.
I do hope that GRRM finishes the books because I still want to read them despite the tv series being over.