The Smothers Brothers?
Tripp and Marvin Weisbord.
Frank Zappa and his guitar/piano.
Burt Bacharach and Hal David.
Ping!
I’m not sure how anyone could rationalize a better, more successful team than Lennon/McCartney.
David Crosby and Graham Nash
Any listing (which I assume is only of the modern era, as Rogers & Hart, Rogers & Hammerstein, Gilbert & Sullivan are not suggested) should include Pomus & Shuman, and John & Taupin.
Rodgers and Hammerstein?
Apost and Rophe
the two dudes from abba.
This answer is more controversial than any politics here
The two were the original founding members of the Top 40 rock group the Turtles. After the Turtles dissolved, Volman and Kaylan first joined the Mothers of Invention as Phlorescent Leech & Eddie.
I never knew they were known by those names. 8>)
The answer to your questions are yes for each of them. Since different styles of music were presented they were all the best in their respective styles, and there are probably more as well. 8>)
Jimmy Webb and himself.
Carole King and herself.
Wait no, they're the greatest pot heads.
Barry Mann and Cynthia Weil. Carol King and Gerry Goffin. Those two pairs were amazing. I’d pick Lennon and McCartney as the top, but it’s a great debate. Elton John and Bernie Taupin deserve mention, too.
It is everybody and nobody...
Robert B and Richard M Sherman
The Sherman Brothers wrote more motion-picture musical song scores than any other songwriting team in film history. Film scores of the Sherman Brothers include Mary Poppins, Chitty Chitty Bang Bang, The Jungle Book (except The Bare Necessities, which Terry Gilkyson wrote), Bedknobs and Broomsticks, The Happiest Millionaire, Charlotte's Web and The Aristocats. Their most well known work, however, remains the theme park song There's A Great Big Beautiful Tomorrow and "It's A Small World After All." According to Time.com, the latter song is the most performed song of all time.