There have been no shortage of villains (at least 8) assuming the alias Clayface. The first Clayface, Basil Karlo appeared in 1940's Detective #40. Although beginning as a simple master of disguise, Clayfaces have since become associated with shapeshifting powers.
1977's The New Adventures of Batman saw the onscreen debut of Clayface. This Clayface, Matt Hagen was actually comic's second Clayface and had the ability to shapeshift thanks to a special potion he consumed.
Matt Hagen returned as Clayface in Batman: The Animated Series though many aspects of the Basil Karlo character were also incorporated.
Clayface's ugly mug returned slightly streamlined for The New Batman Adventures.
The 1999 animated Batman Beyond series adapted many classic Batman rogues to the futuristic setting. Although Clayface did not appear, the character Inque displayed similar shapeshifting abilities.
On the live action Birds of Prey an incarcerated Clayface was responsible for assassinated Catwoman at the request of the Joker.
The Batman introduced a new Clayface to Batman lore. Ethan Bennett, friend of Bruce Wayne and police officer was turned into Clayface by exposure to the Joker's chemicals at the end of the first season. Tragically, he was never able to reform.
In the fourth season of The Batman, a second Clayface was introduced. For the first time onscreen, the Clayface was named Basil Karlo. During his first appearance, the two Clayfaces clashed in a big muddy mess.
In the Joker: The Vile and the Villainous episode of Batman: The Brave and the Bold, the Preston Payne version of Clayface (comics third Clayface) appeared as an Easter Egg in the villains bar.
In 2011, the Young Justice animated series had the young heroes nearly overcome by the Matt Hagen Clayface in the opening seconds of Downtime.
In 2012, Batman himself will become a "clayface" thanks to stop motion animation by Aardman Studios featured as a set of DC Nation shorts.