In the United States, "I saw you on the TV" is wrong. "I saw you on television" or "I saw you on TV" are both natural, and I can't say which is more common.
An old Mickey Mouse song has Mickey singing "I'm a happy mouse/And I ought to be/'Cause you let me in your house/And watch me on TV."
In a famous George Carlin monologue, he says "There are 400,000 words in the English language, and there are seven of them that you can't say on television."