In DragonVale for the iPhone and iPad, the Century Dragon is a limited dragon and is the 100th dragon to be released in the game (which is why it's the Century Dragon). It was released in February of 2013 it isn't known how long it will be available, so breed it while you can.
The Century Dragon has a base breeding time of 10 hours, sells for 1,500,000 coins, and earns 100,000 XP for successful breeding.
To breed a Century Dragon, you just need to breed any dragons that contain a total of cold, earth, and water attributes. Breeding a Cold Dragon with a Mud Dragon, or a Snow Dragon with a River Dragon seem to be good combinations.