The series finale is the most sacred thing there is when it comes to television - and the more emotional they are, the better. A show could have 10 brilliant seasons, but if the writers don't stick the landing, all that goes down the drain (just ask Game of Thrones). TV finales don't need to make us weep to be considered a "good" finale, but bringing us to tears is a great way to prove how connected we were to that story and the characters.
The final scene is usually reserved as an epilogue to a big climax. It usually isn't action-packed or dense with plot, but it's a bridge to wrap up any last thoughts or moments that will prepare us for the end. Whether they use that final moment to say their goodbyes or answer one last question, these series all did it right. It makes it so much easier to go back and binge through our favorite show when we actually look forward to the ending.