The dragons actually stick around if you beat the game, and they attack fairly often. I remember in Oblivion, the Oblivion gates would be gone forever if you beat the main quest, so that was a bit of a bummer.
I don't think there's anything that goes away when you beat Skyrim, except Alduin.
When I played Skyrim I think the main quest was one of the first things I beat. I just kinda wanted to see what happened I guess. On newer characters, I could be less bothered beating it, because unfortunately the main quest isn't as good as it ought to be.