I'll do this just through performances.

Radiohead performed with R.E.M.
R.E.M. performed with Bruce Springsteen
Bruce Springsteen performed with Eric Clapton

Primal Scream to Eric Clapton

-Gary Mounfield is the current bass player for Primal Scream.
-Mounfield was the bassist for Stone Roses
-Stone Roses singer Ian Brown has worked with Noel Gallagher
-Gallagher's band Oasis have covered The Beatles on several occasions
-Eric Clapton guested on While My Guitar Gently Weeps by The Beatles

Steven Wilson to Eric Clapton

Alex Lifeson of Rush played with Steve Wilson on the song "Anesthetize" from 2007s "Fear of a Blank Planet".
In addition to guitar, Alex Lifeson is an accomplished Mandolin player, an instrument that is often used by R.E.M. guitarist Peter Buck, notably on the track "Losing Mr Religion" from 1991.
R.E.M. has toured with Bruce Springsteen
Bruce Springsteen has performed with Eric Clapton

Cake to Eric Clapton

-Cake toured with Cheap Trick
-Cheap Trick's drummer Bun E. Carlos is currently in the supergroup Tainted Windows with Taylor Hanson, James Iha and the bassist for Fountains of Wayne
-James Iha's band A Perfect Circle featured Tim Alexander as their original drummer
-Tim Alexander has collaborated with bass virtuoso Tony Levin
-Tony Levin played bass on Pink Floyd's album A Momentary Lapse of Reason, in the place of Roger Waters
-Water's solo album Pros and Cons of Hitchhiking features guitar work from Eric Clapton

John Cale to Eric Clapton

Lol at Taylor Hanson.

Anyway, this one's easy.

John Cale was in The Velvet Underground with Lou Reed
Lou Reed worked with David Bowie on his album Transformer
David Bowie and Dave Gilmour have played live together
Dave Gilmour and Brian May have collaborated with eachother
Brian May played with Eric Clapton at the Freddie Mercury Tribute Concert in 1992

Buddy Rich to Eric Clapton