Bill Bruford left Yes in 1972 to join King Crimson
When Crimson split in '75 (I think), Bruford played drums for Genesis on tour after Phil Collins took over vocal duties from Peter Gabriel
Both Bruford and Collins were involved with a jazz-fusion outfit called Brand X in the 70s
Genesis guitarist Steve Hackett and Yes guitarist Steve Howe were members of a band called GTR in the 1980s
Jon Anderson guested on Crimson's "Lizard" album in 1971
Steve Howe and former Crimson bassist John Wetton (as well as ELP drummer Carl Palmer) were members of Asia
John Wetton was featured on Steve Hackett's Genesis Re-visited
Robert Fripp (Crimson guitarist) played on a song or two on Peter Gabriel's first album
Steve Hackett and Yes bassist Chris Squire are supposedly involved in a collaboration project called "Squackett" (seriously)
I saw a video on youtube where Hackett and Yes keyboardist Rick Wakeman were playing what looked like an improv, I believe it was a show called Gastank
So yes, those bands definitely ran in the same circles it would seem. ELP was also connected to a lesser extent.