One of the best things in Skyrim is how you can completely ignore all about the main quest like dragons, dragonborn, shouts, etc and play your character without feeling like you're the chosen one (if that's what you're looking for).

I'm currently playing a sneaky dunmer and when I left Helgen I passed right through Riverwood without speaking to anyone and headed straight to Whiterun. That means I'm now 31 hours in and no one I talked to has ever mentioned dragons or the dragonborn. This is exactly what I wanted because this character is just an avarage dark elf trying to escape the hell that Morrowind has become after the eruption of the Red Mountain.

Do you have any characters that also is not a dragonborn? Tell your story.

I have played with 3 characters so far and only my first character, my Nord was the Dragonborn. My current character, Link is a Bosmer who was a young thief during the time of the Oblivion crisis. Sometime after he drank a potion that servilely slowed down his aging process. He is now at the end of his life, old and grey he made his way into Skyrim. I'm only a few hours into the game so his path is still unknown.

Cool backstory, no need to include the potion thing tho. Elves can live for centuries, well at least dark elves can.

But I like my Dragonborn's story! http://i639.photobucket.com/albums/uu116/furnishn/9fe9d99c.jpg, deserted his post in Morrowind and tried to flee to Skyrim. Ended up finding the Blades, and led them to victory over Alduin's dragons and other foes.
I do have an http://i639.photobucket.com/albums/uu116/furnishn/1080952c.jpg http://i639.photobucket.com/albums/uu116/furnishn/5ba6ed26.jpg though, whos story involves stealing to survive as a child, then being inducted into the thieves guild. He accidentally killed someone during a home invasion in Cyrodiil, found some sick satisfaction in it, and continued doing it until the heat on him was so great he had to flee the country and tried to cross over into Skyrim.