There's a one-shot band called "Bloodline" with Waylon Krieger (of Robby), Erin Davis (of Miles), and Berry Oakley Jr. Good blues-rock, Joe Bonamassa on guitar.

Various bands with Jason Bonham and/or Zakk Starkey. Probably a bit sketchy to find anything really good there. Paul's son James McCartney has an EP just out, and there's also Julian and Sean Lennon, if those fit your tastes.

Derek Trucks far exceeded his uncle Butch, IMO. John Lee Hooker Jr. has a couple of decent albums. Rufus and Martha Wainwright also come to mind.

Sting's son has a band who opened for the Police when I saw them a few years ago. The son's band sounded the same on all songs. And sucked.

Speaking of sucked, don't forget Wilson Phillips, Miley Cyrus, and Kelley Osbourne. ;)