I've just been listening to all the Beatles stuff we have again (ok, 2 CDs), and I was looking out for vocal harmonies. Someone on here, Slacker or Chris, said something about "good backing vocals making a band", and I had always heard the Beatles had good harmonies.
So I listened for them. Sometimes, it was obvious, like on Help!. But are there harmonies in the verse of Something, or is it just echo? There are loads of places where I can't hear a second voice, but suspect it's there anyway.
What albums do you have? Rubber Soul has plenty of harmonies. You should be able to tell pretty easily when they're doing it and when they aren't. It's basically the difference between you playing a single note on the guitar and playing a chord - it sticks out.
The beatles were studio magicians - they invented a WHOLE load of recording techniques, if there is a trick to making something sound good they'll do it. From that perspective there is probably a lot of double tracking of the vocals whic will make them feel more "full" without you really notcing. They may also use some effects subtly, maybe putting a bit of reverb on the vocals, or delay (but quietly), potentially even putting some chorus in (not sure about this one though). Which specific songs/albums are you thinking of?
I have their Number Ones album, and Let it Be... Naked (which I think stripped off all the wall of sound stuff). For example, on Something, at the "You're asking me, but I don't know", there's clearly two different voices. In the first verse, "Something in the..." it sounds more like reverb. At the "don't wanna leave you now", I'm more unclear.
The earliest stuff is actually kinda lacking in the complexity factor of harmonies. Likes of parallel 5ths, but I mean, its not like it sounds bad. But, as time went on, they improved 100x in the vocal harmony section.

I love me some beatles.