Are the dragon-born all gone? (at least after your death)
Will we see them in future games?
Granted i have not completed the MQ so if there's anything explaining how there will be more please tell me.

The dragon born and alduin marry and have loads of little dragonborns.
Once you complete the main quest you basically start a family simulator

If you read the book of the dragon born theres a small hint. It does say that since its a bloodline, it's completely logical to assume there would be two or more at a time (the emperor plus any sons/daughters they produce), but since we are dealing with an imperial hierarchy, the notion that there is only one true heir and one true of the dragon born is put forth to the people of the empire. It's overall a mystery how many there are currently if there are any, though as the above poster mentioned, having yourself a family would of course change that.

Dragonborn is a gift (bad example but kind of like the "Shining") Anyone could be a Dragonborn. As for if we will see them? Not a clue. Probably not, and we probably won't see dragons again either. They were more plot integral than most things.

It is, however, also stated that (akatosh?) choses a mortal. So it doesn't have anything to do with blood-line, but to be chosen by (akatosh?).

Ninja'd.