Perhaps here it would be more relevant to mention everyone who was influenced by the Beatles rather than who influenced them. But that would make this go on for pages and pages... Let's face it, nearly every band or artist who has been making music since 1960 cites those British boys as an important influence.
Their songs have been covered countless times and have skyrocketed unknowns into fame or rejuvenated old acts. They have shown up in the theme songs of TV shows, the credits of movies, and on every DJ's track list. The Beatles' songs are inescapable. They are as imbedded into our culture as Elvis, perhaps even more so, and are as well known as Cheerios and Wonderbread (and they weren't even Americans!).
On his own personal influences, along with explaining that he liked to write purposely vague lyrics "á la Dylan," Lennon said
"Only dead people in books. Lewis Carroll, certain paintings. Surrealism had a great effect on me, because then I realized that my imagery and my mind wasn't insanity; that if it was insane, I belong in an exclusive club that sees the world in those terms. Surrealism to me is reality. Psychic vision to me is reality. Even as a child. When I looked at myself in the mirror or when I was 12, 13, I used to literally trance out into alpha. I didn't know what it was called then. I found out years later there is a name for those conditions. But I would find myself seeing hallucinatory images of my face changing and becoming cosmic and complete. It caused me to always be a rebel. This thing gave me a chip on the shoulder; but, on the other hand, I wanted to be loved and accepted. Part of me would like to be accepted by all facets of society and not be this loudmouthed lunatic musician. But I cannot be what I am not."