Gregg has written hits for Sam Brown ("Stop!"), Joe Cocker ("Tonight" and seven others) and contributed songs to Maria McKee, Lone Justice, Beth Hooker, Carla Olson, Papa John Creach, Jeff Healey, Nelson, Curtis Stigers (together with Shelly Peiken), Lola Thomas, John McVie, Percy Sledge, Andrew Strong, Matraca Berg, Billy Ray Cyrus, Charles & Eddie, Tal Bachman, O-Town, Thick Pigeon, Ane Brun, Joe Bonamassa, Heather Small, John Farnham, Swirl 360, Chris Thompson, The Commitments, Carmen Rae, Aurical, The Human League, Tom Jones, Beth Hart, Teresa James, The Nighthawks, Andy Griffith, Edgar Winter, Bloodline, Del McCoury, Ray Stevens, Jason Ringenberg, Paul Adkins, Timothy B. Schmit, Consoul Trainin, Kris McKay, Chris LeDoux, Phyllis Brown, Shannon Curfman, Eric Burdon.
During the 1980s he played bass for Bob Dylan on Real Live (1984). He also played bass for Barry Goldberg, Sass Jordan, Carla Olson, Mick Taylor, Dave Alvin, Coup de Grace, The Pets, KGB (along with Carmine Appice), Tony Gilkyson, Avery Sharpe and Katy Moffatt.
He is also featured on The Rolling Stones' Lost & Found Vol. 2 on the track "Tombstone Blues" along with Carlos Santana, Bob Dylan, Mick Taylor, Colin Allen and Ian McLagan.
He also released a solo album, called Soft as a Sidewalk (1979).
He was the musical director for Andy Kaufman's show at Carnegie Hall in 1979. He is also featured in the 1980 movie Andy Kaufman Plays Carnegie Hall and as an actor in the motion picture Man on the Moon, starring Jim Carrey. He's up to appear in the 2015 documentary Kaufman Lives.
Gregg sings on two songs on the 2015 album by Paul Jones (Manfred Mann) Suddenly I Like It.