Paperback Writer is more of a McCartney song, I think. He who sings lead is the main or sole writer, is the rule of thumb.
Me? I was pleasantly surprised to see someone else nominate “I Feel Fine”, pretty much my favourite Beatles track but one which many people would dismiss as bubblegum.
Also For No One, Hey Jude, In My Life, I’ll Be Back, If I Fell. Most of the songs that start with the letter I, actually.
“Tomorrow never knows” this was so many years ahead of its time.
And here I was thinking NOBODY will vote for Tomorrow Never Knows, which actually receives my vote as favorite/best Beatles song.
…Lay down all thought and surrender to the void…
I am pleasantly surprised to see NO ONE said “Hey Jude.” For some reason, that one seems to be constantly at the top of radio “Top songs” lists, but I totally can’t get the appeal.
My favorite (bearing in mind that I only know their big hits)? Yesterday.
Apart from Ximenean, of course. 
I like “Hey, Jude”, but it’s not my favorite. Nor is “Eleanor Rigby”–although it’s in the top 10.
I like “I’m So Tired” best, (I think–this changes every day and I tend to prefer Lennon to McCartney in many ways), but I’m going with “Money”.
They were so varied, rich and deep, there’s no way to pick just one…
“She Came In Through the Bathroom Window” or “Here Comes the Sun.”
This would be my choice if I didn’t think it was cheating.
For a single song, I’m inclined to go with “A Day in the Life,” though for full effect it has to be heard at the end of Sgt. Pepper.
For what it’s worth, “A Day in the Life” won the March Beatle Madness Tournament (opening round here).
I’d pick the Abbey Road medley.
For a single song, it’s impossible to decide, and, of course, I’ll change my mind tomorrow, but for now, I’ll go with “Got to Get You Into My Life.”
I might go for “Penny Lane” although “Eleanor Rigby” is unforgettable. It’s not a Beatles song as much as a solo with strings so in some ways it’s too much of an outlier to count.
‘I want you’. Definately.
A Day in the Life.
The great thing about the Beatles is that even if you can’t agree about what the best song is, it’s hard to discount anybody else’s opinion because so many of their songs are that good.
ANYTHING from the Revolver era (that includes Rain.)
Since I have to pick one, I’ll go with She Said She Said.
I vote for Paperback Writer, followed by Hard Day’s Night, Hey Jude, and Sgt. Pepper’s Lonely Heart’s Club Band.
Sexy Sadie, with The Ballad of John and Yoko coming in second.
Strawberry Fields Forever if for no other reason then for this:
Also, here’s a tournament you might find of interest:
Beatle Madness Rd 1
Beatle Madness Rd 2
Beatle Madness Rd 3
Beatle Madness Rd 4
Beatle Madness Rd 5
Beatle Madness Championship Matchup
Agreed that it’s almost impossible to pick just one, and that it can easily change from day to day.
Today, though, I think I’ll go with “Revolution”.
They have so many good songs it’s hard to choose.
Elenore Rigby hasn’t been mentioned yet but I think my favorite is Yesterday. With a Little Help From My Friends aint bad either.
Well, the OP asked for the “best,” not our “favorite.” So one of my “favorites” is:
Ob-La-Di, Ob-La-Da . . . only because nobody else will mention it. It’s a song I never think about until I hear it, then I love it . . . then forget about it again.