Incredibly difficult for me to do this, but I'll give it a shot.
1. Sgt. Pepper's Lonely Hearts Club Band (Easy first for me. This whole album means so much to me, as it tells an all-encompassing story. All Beatles albums are incredibly true, but this one takes first for me. If you would like to read my interpretation of what this album means, let me know. Bobber mentioned that you typically are not interested in those kinds of things.)
2. Let It Be (Lyrically, Dig a Pony is my favorite Beatles song. This album is my favorite album to play in the car.)
3. With the Beatles (Out of the earlier albums, this is my favorite. The lyrics are so true. The only song I don't care for is Money.)
4. Revolver (Amazing, complex musical album. I love to play/sing I'm Only Sleeping on the guitar.)
5. Magical Mystery Tour (I'm counting this as an album, regardless of what you 'technical' people say. The songs on this album flow very well, almost as well as Sgt. Peppers.)
6. Help (I love this album, and the movie.)
7. Abbey Road (Best closing sequence to any album, all time.)
8. Rubber Soul
9. A Hard Days Night
10. Please Please Me
11. Beatles For Sale
12. The White album (This album is incredible, but I ranked it low because there are several songs that I really do not enjoy listening to in any situation.)
13. Yellow Submarine
Agghh, it's so hard to hit post because I love every album! For the spirit of this thread, I must do it!