Breaking away from the Beatles for a bit, Beginners can learn "Fisher's Hornpipe," a timeless dance tune.
For Advanced players, learn to play diatonic harmonica on a tune widely known for the chromatic harmonica: Stevie Wonder's "Isn't She Lovely," Part 1 and Part 2.
And, just for fun there's a performance of "I'm an Old Cowhand," complete with proper headwear!