You posted this right as I'm in my height of Beatles fanhood. I've been listening to Rubber Soul, Revolver, The White Album, Sgt. Pepper, Abbey Road, and Let it Be nonstop.
Those are the albums I've heard the most of, and the most of to judge. I'll go through each:
Rubber Soul: Very good, probably the first one where the Beatles start to get serious. However, it still has hints of the early Beatles stuff, so in the end I find that its good but not as good as the others...
Revolver: Great album. It has so many great songs on it (Taxman, Eleanor Rigby, I'm Only Sleeping, Love You To, She Said She Said, Tomorrow Never Knows) and definetely one of my favorites which contains some of my favorite songs, but it has a few songs on it which I don't care too much more. No bad ones, but there are a few OK ones.
Sgt. Pepper: Sort of like Revovler, it has alot of great songs but a few that are just OK. Really it seems to have less OK songs than Revolver does (IMO), but I still hold it in the same regard as Revolver - very very good but not my favorite.
The White Album: Probably my favorite Beatles album. I don't see how anyone cannot choose this one, since it just has so many songs! Its a double album so its almost not fair. But there are so many great songs and then so many very good songs that its hard not to pick it. I can't think of a single bad song on it, even a single "OK" song. Every song is great...
Abbey Road: Another great album. Almost as good as the White Album, but it falls short because it has fewer songs (IMO). The medley at the end is great (I find myself singing Mean Mr. Mustard through You're Gonna Carry that Weight way too often) and the songs at the beginning are just as good...A great album all around.
Let it Be: Very good. Not as great as Abbey Road or Sgt. Pepper, IMO, but good nonetheless. Let it Be Naked is the one you should get, IMO, because the songs sound much better without the overdone theatrics - especially since their idea was to make a stripped down Beatles album.
So, in short, I think the White Album is the best, with Abbey Road and Revolver close, Sgt. Pepper very good, and Let it Be and Rubber Soul also good.
I still have to listen to Yellow Submarine, since its the only other "serious" Beatles album I haven't listened to since I began to notice (it probably got played when I was little but not since I've grown up and really started to like music).