Can you ride a dragon on dragon age origins

No, unfortunately you cannot ride on a dragon in the game. You get to kill a few dragons, like when you have to face Flemmeth, or the Andraste occult during your Haeven mission, and then you also have the Arch Demon at the end.
It would have been fun to have been able to ride on dragons, but the game also says, while loading, Grey Wardens used to fly on Griffins, but Griffins were wiped out.
Still, it's an awesome game!!