I think I read somewhere that it wasn't Ringo, and that it might not even have been a "Hammond Organ" (which I think is what it was called on the sleeve of my LP a long time ago).
It also doesn't sound like Ringo's style ... IMHO!
I'm sure someone more knowledgeable can do this one better than me.
I love John, I love Paul, And George and Ringo, I love them all!
An organ isn't even audible on the track. Some interesting thoughts here, where someone is suggesting that the song could be a solo recording by Paul: http://dmbeatles.com/forums/b-songs/m-1127812686/
I distinctly remember reading that on the back of Rubber Soul (Capitol US version) when it came out in December of '65, and thinking "that's ringo?" --the Hammond organ ?
The loud organ stabs do sound a bit odd I think. In fact one time I had this track playing and a friend of mine thought the organ stabs were funny, saying it made the song sound "dated". After that I always focused on that and wished that guitar licks had played the organ part instead.
"Dont take life seriously, you'll never get out of it alive"