Dragons cannot be truly "tamed", but they can be bonded with and trained. The Valyrians rode dragons for millennia. Aegon I Targaryen and his sister-wives, who descended from Old Valyria, used the last three dragons in the world to conquer and unify the Seven Kingdoms.
Dragons are fairly intelligent animals, and like a horse or a dog, they can be trained by their rider to respond to basic voice commands. Tyrion Lannister claims that dragons are intelligent, much more so than most people and will quickly recognize friend from foe. If they are not trained they will quickly lay waste to anything around them. The key to training dragons is making sure they are well fed, a dragon with a full stomach is more obedient. Since they cannot be truly tamed, dragons can be very dangerous even to their riders. However, they can form very strong bonds with their riders and will show affection and trust towards them. They will even nuzzle their riders, hoping to be petted.
Daenerys Targaryen has trained her three dragons to respond to vocal commands in her mother tongue of High Valyrian. She often uses the command "Dracarys" (Valyrian for "dragonfire"), to which her dragons respond by instantly breathing fire and burning anything in their path.
In the books
In the A Song of Ice and Fire novels, additional known dragonriders are:
|Aegon the Uncrowned||Quicksilver|
|Daeron the Daring||Tessarion|