A little bit of Texas trivia: On August 10, 1996, KTCY-FM began its broadcasting activities under the name "Fab 105", broadcasting all-Beatles music. I recall that it was commercial free, but I could be mistaken on that. Sadly, it is long gone. (It is now a religious station.)
It was the first [Dallas - Fort Worth] Metroplex station to be fully programmed from computer hard drives ... the station ran jockless through 1997.
http://en.wikipedia.org/wiki/KZMP-FM#HistoryHere's my personal list. They are loosely ranked, but it's really hard to definitely say that I like one more than another of these. I also like a lot of the early Rock and Roll music the Beatles covered.
Penny Lane - Magical Mystery Tour (1967)
Yesterday - Help! (1965)
Michelle - Rubber Soul (1965)
Hey Jude - Hey Jude (1968/1970)
Let It Be - Let It Be (1970)
While My Guitar Gently Weeps - The White Album (1968)
Blackbird - The White Album (1968)
She's Leaving Home - Sgt. Pepper's Lonely Hearts Club Band (1967)
Eleanor Rigby - Revolver (1966)
Lady Madonna - Hey Jude (1968/1970)
Lucy in the Sky with Diamonds - Sgt. Pepper's Lonely Hearts Club Band (1967)
Strawberry Fields Forever - Magical Mystery Tour (1967)
A Day in the Life - Sgt. Pepper's Lonely Hearts Club Band (1967)
Come Together - Abbey Road (1969)
Here Comes the Sun - Abbey Road (1969)
Can't Buy Me Love - A Hard Day's Night (1964)
All You Need is Love - Magical Mystery Tour (1967)/Yellow Submarine (1969)
Norwegian Wood (This Bird Has Flown) - Rubber Soul (1965)
This is not my list, just a Listmania list I found. It includes some post-Beatles tracks by Beatles members as well.
1. Here Comes the Sun - Abbey Road (1969)
2. Imagine - Imagine by John Lennon (1971)
3. Hey Jude - Hey Jude (1968/1970)
4. A Day in the Life - Sgt. Pepper's Lonely Hearts Club Band (1967)
5. All You Need is Love - Magical Mystery Tour (1967)/Yellow Submarine (1969)
6. Eleanor Rigby - Revolver (1966)
7. Michelle - Rubber Soul (1965)
8. Back in the U.S.S.R. - The White Album (1968)
9. God - Plastic Ono Band by John Lennon and Yoko Ono (1970)
10. I Want You (She's So Heavy) - Abbey Road (1969)
11. I Am the Walrus - Magical Mystery Tour (1967)
12. Can't Buy Me Love - A Hard Day's Night (1964)
13. Tomorrow Never Knows - Revolver (1966)
14. Blackbird - The White Album (1968)
15. Yesterday - Help! (1965)
16. Let It Be - Let It Be (1970)
17. Twist & Shout - Please Please Me (1963)
18. All My Loving - Meet the Beatles! (1964)
19. Golden Slumbers/Carry that Weight/The End - Abbey Road (1969)
20. I'll Follow the Sun - Beatles for Sale (1964)
21. Drive My Car - Rubber Soul (1965)
22. Within You Without You - Sgt. Pepper's Lonely Hearts Club Band (1967)
23. Maybe I'm Amazed - McCartney by Paul McCartney (1970)
24. Watching the Wheels - Double Fantasy by Yoko Ono (1980)
25. Across the Universe - Let It Be (1970)
26. Hey Bulldog - Yellow Submarine (1969)
27. While My Guitar Gently Weeps - The White Album (1968)
28. Strawberry Fields Forever - Magical Mystery Tour (1967)
29. You Never Give Me Your Money - Abbey Road (1969)
30. I'm Only Sleeping - Revolver (1966)
31. In My Life - Rubber Soul (1965)
32. She's Leaving Home - Sgt. Pepper's Lonely Hearts Club Band (1967)
33. Live and Let Die - Live and Let Die by Paul McCartney (1973)
34. Mind Games - Mind Games by John Lennon (1973)
35. Happiness is a Warm Gun - The White Album (1968)
36. I Want to Hold Your Hand - Meet the Beatles! (1964)
37. What is Life - All Things Must Pass by George Harrison (1970)
38. Isolation - Plastic Ono Band by John Lennon (1970)
39. Singalong Junk - McCartney by Paul McCartney (1970)
40. Because - Abbey Road (1969)
41. Girl - Rubber Soul (1965)
42. Lady Madonna - Hey Jude (1968/1970)
43. The Girl is Mine/Say Say Say - Thriller (1982)/Pipes of Peace by Paul McCartney (1983)
44. I Saw Her Standing There - Please Please Me (1963)
45. Dear Prudence - The White Album (1968)
46. I Want to Tell You - Revolver (1966)
47. Sgt. Pepper's Lonely Hearts Club Band - Sgt. Pepper's Lonely Hearts Club Band (1967)
48. Wonderful Christmastime - Back to the Egg by Paul McCartney (1979)
49. Got My Mind Set on You - [cover version by George Harrison] Cloud Nine (1987)
50. Come Together - Abbey Road (1969)
Honorable Mention: Good Night - The White Album (1968)
Honorable Mention: Hello, Goodbye - Magical Mystery Tour (1967)
source for the list: A Listmania! list by Jordan Hubert (California)