All four members of The Beatles became involved in the film industry in one way or another. The whole band famously played versions of themselves in the music films "A Hard Day's Night" and "Help!," and collaborated on several other Beatles film projects besides, but they also split off to work on individual movies as well.
John Lennon appeared in Richard Lester's "How I Won the War" in 1967, and directed and produced many experimental shorts. He famously recommended that the Beatles' manager, Allen Klein, buy the rights to the trippy acid Western "El Topo."
Paul McCartney, likewise, produced some shorts and appeared in films like "Eat the Rich" and various animated shorts. He also had fun cameos in "Pirates of the Caribbean: Dead Men Tell No Tales," "Spinal Tap II: The End Continues," and several others.
Ringo Starr was the most prolific actor of the band, appearing in a wide variety of fun fringe movies like "Candy," "The Magic Christian," "200 Motels," "Son of Dracula," and "Lisztomania." Even if Starr had never been in the Beatles, he would still be a notable cult film figure. He was even in an episode of "Sabrina: The Teenage Witch."
George Harrison, meanwhile, was perhaps the most commercial producer and/or executive producer of the band, having backed some rather remarkable movies. He stumbled his way into producing "Monty Python's Life of Brian," which led to his collaboration on several additional Python projects. He produced "Mona Lisa," "Withnail & I," and "How to Get Ahead in Advertising." He clearly had the best taste of the Beatles.
So when Harrison said, in a 1988 interview with Film Comment, that his favorite comedy was Mel Brooks' 1967 film "The Producers," you can be sure he knows what he's talking about.