Interestingly, I have to go down quite far on my list of favourite Beatles songs before I hit a Lennon/McCartney collaboration. Most of my favourites are either McCartneys (Golden Slumbers medley, Hey Jude, Let It Be, Blackbird, Here There & Everywhere, Lovely Rita, I Will), Lennons (Across the Universe, Strawberry Fields Forever, Dear Prudence, Don't Let Me Down, I Am the Walrus, I Feel Fine, Real Love), or Harrisons (While My Guitar Gently Weeps, Here Comes the Sun Something).
I'm not really sure if this can really be considered a Lennon/McCartney collaboration (there is a lot of controversy surrounding the authorship), but it might be "In My Life" for me. After that, it would be "Baby You're a Rich Man."
For my least favourite Lennon/McCartney: "I Wanna Be Your Man." Ee. I think we would have been better off if they would have just let Ringo write a song instead. Horourable mentions: "Love Me Do," and if it is a Lennon/McCartney composition, "One After 909." After watching Let It Be, I would have to agree with what Paul said about why they never recorded it before: the lyrics were terrible. Looks like they didn't re-write it.