The Beatles are the greatest! If you want some songs, first you should decide where you wanna start from them? (Beatlemania Days, Help/Revolver Days, Hello Goodbye Pre Hippie, Let it Be/The End)
Beatlemania has good catchy songs like "I wanna hold your hand" and "She loves you". Theres also "Cant buy me love" and "Hard Days Night", the latter of which was a really succesful movie.
Now on to the 65/66 days. You know "Yesterday" so if you like Paul, I reccomend "Eleanor Rigby" which is sad and beautiful at the same time. Of course there's "Help!" which was also a good movie. Check out the album "Rubber Soul" to.
Pre-Hippie days were kinda like "Magical Mystery Tour" (again another movie) with albums like "Sgt Peppers Lonely Hearts Band" which is considered one of the best albums ever made! One famous song? "I am the Walrus"!
And then we have the end, as I call it. Some of the best songs like "Hey Jude" and "Let It be" came out. Also, if you like murderous songs about hammers, "Maxwell Silverhammer" is for you!
Some other songs not mentioned above:
"Girl"- A beautiful song by John. So sweet.
"Eight Days A Week"- Catchy as heck.
"All My Loving"- I heard it in "Hard Days Night" and I was amazed.
"If I Fell"- Sweet little ditty.
"I wanna be your man"- Kinda more "edgy" in a way!
"Lucy in the Sky W/ Diamonds"- Trippy. =p
"Yellow Submarine"- Yeah finally they let Ringo sing!
"Ticket to Ride"- From "Help!", it's sweet and lovable.
"Twist N' Shout"- Early on in the band.
"Day Tripper"- I love the guitar riff in it!
If you wanna get a more modernized take on some of these songs, go see "Across The Universe". But always listen to the classics!