I'll go first.

After uniting Skyrim by convincing both Imperials and Stormcloaks he was on their side and using the opportunity to kill off both, The Dragonborn then starts up a Skooma ring. With the Thalmor getting int he way of profits, he decides to throw them out of Skyrim once and for all, but on his way to the Embassy, an ebony clad Bosmer warrior appears. He calls himself Gaenor, and says his spirit has been rematerializing a long time after his defeat at the hands of The Nerevarine. The Dragonborn finds himself severely outmatched and falls to Gaenor's sword.

If Bethesda isn't going to finish it, I can imagine anything I want.

He will be corrupt by Herma mora and jump off the summit of Apocrypha.

The Dragonborn will somehow continue his journey into the next game, as my character was the CoC before re-entering his homeland of Skyrim after 200 long years of hiding once he contracted vampirism.

As a vampire he'll be surviving until the end of time by feeding and feeding, waiting for a human to kill him, as only humans can truly hope to kill monsters.

He ventures off to somewhere and never returns.

I think he'll end much like...

('Pirates of the Caribbean spoiler ahead.)

...Orlando Bloom's character does. He'll be bound by Mora to preserve his life.

He will dissapear off the face of Mundus

1000th Post What a Joyous occasion

He disappears in Apocrypha, never to be seen again. And the skaal tell the tale to their kids. The nighttime story of the "Last Dragonborn". Who will appear when the moons eclipse. and enslave the souls of mortals. You will know him when he appears, when you see a writhing mass of tentacles consume you... or so the legend goes...

S/he builds a homestead, adopts some kids and enjoys a peaceful life. Mostly.

He becomes a drunk in Riverwood telling anyone who will listen about all the great and wonderful things he did. Most people will just mutter something about stupid town drunk, and toss a coin to get him to leave them alone.