"Watching cartoons, movies, and dramas develops the human brain." Would be the correctly structured sentence. "Watching" is the subject of the sentence, so the verb is singular: "develops".
A series such as "cartoons, movies, dramas" normally has "and" before the last item in the list. The comma after "movies" is optional, depending on location (UK, USA, etc.), style book (if any) used, and personal preference. (Whether to place a comma there is actually the subject of huge debates!)
But you could also say: "Cartoons, movies, and dramas develop the human brain." Here the phrase "Cartoons, movies, and dramas" is the subject, so the verb is plural; "develop".