When do you fight the dragons in dragon age origins

Many times! It really depends what you mean! Drakes can be found in the tower of magi during the quest where you clear it out and during the urn of sacred ashes quest. Dragons can be found during the last 2 quests I mentioned and in the nature of the beast quest. HIGH Dragons can be found near the end of the urn of sacred ashes quest where you see a gong, and flemeth is also a high dragon when you do morrigans personal quest. Finally you fight the archdemon at the end who is also a dragon.