For Ringo, I'll choose "Boys" too. There's just something awesome about the way he delivers it! Almost swoon-inducing...
For George, it's a toughie, 'cos you've kinda got the early, thick, untrained George voice, and the later, developed, melodic George voice. Out of the earlier songs, I'll go with "Do You Want To Know A Secret". Later songs, I'll choose "I Me Mine".
For Paul, I think I have to divide it between his "Little Richard-esque screamers" and his "softer melodic" songs. For the screamers, it's definitely "I'm Down"... Can't get enough of that voice! And for the softer ones, though there are MANY... oh bugger it, I can't choose one.
For John, I can definitely split it between a rocker and a softie... The rocker has to be "Bad Boy". Those screams... deary me! And the softie is probably "Ask Me Why", even though "Across The Universe" is actually my fave Beatles song. There's just something about the delivery of "Ask Me Why" that gets to me more.