[QUOTE=42fish]
Father/Son
Don Cherry (jazz trumpeter)/Eagle Eye Cherry (“Save Tonight”)
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You could also do Father/(step)Daughter for Don and Neneh Cherry
[QUOTE=42fish]
Mother/Daughter:
June Carter Cash/Carlene Carter
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Actually, Carlene Carter is third generation: Mother Maybelle Carter of the Carter Family!
No mention of the Judds?
Adrian Bellew’s best single, IMO, was “Ooh Daddy,” a duet with his daughter.
Donovan’s son, Donovan Leitch, was briefly a member of the Wallflowers.
Rufus Wainright, in addition to being Loudon’s son, is also the son of Kate McGarrigle, and his sister’s mom is Suzzy Roche of the Roches.
There’s also Jim Croce and his son AJ Croce. Never heard what AJ sounds like though.
Ah! Knew there was another obscure Finn-related one:
Richard Thompson -> Teddy Thompson (his mother is Linda Peters/Thompson)
Mel Tillis (father) and Pam Tillis (daughter)
Naomi Judd (mother) and Winona Judd (daughter)
Alan Osmond (Father) and 2ndG (Eight, count them eight Osmond sons)
On that I originally thought was father/son, but I learn from Wikipedia is actually Uncle/Nephew is Butch Trucks, one of the founding members of the Allman Brothers Band, and his nephew Derek Trucks, member of the Allmans since 1999 and leader of the Derek Trucks Band.
James Raymond was adopted and didn’t know his father was David Crosby until 1995. They have been playing together for years in Crosby’s band CPR.
And of course, who can forget Franz Xaver Wolfgang Mozart’s timeless works 
Cheap Trick has nearly replaced themselves in terms of numbers of offspring in bands.
Rick Nielson’s sons Daxx and Miles were in a band called Harmony Riley.
Robin Zander’s daughter is in a band called The Snaggs, and from what I hear, they’re pretty good.
Jim Dickinson, who is semi-famous in some circles for his production work with Big Star, etc. (he also played piano on the Stones’ Wild Horses) has two sons that are members of the North Mississippi All-Stars.
[QUOTE=Dr. Rieux]
Speaking of Beatles, George and Dhani Harrison.
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I came in to mention Dhani, who looks so much like his father, it’s scary.
I know Dhani has played guitar on other artists’ albums, but has he ever released material under his own name?
Rick Wakeman and Adam Wakeman. I also think another son of his is also a rock ‘star’; I want to say Oscar, but I’m not sure.
Hats off to Roy and Nick Harper.
Edgar Froese of Tangerine Dream brought his son Jerome into the band.
So did Francis Decamps of French prog band Ange (big in France, not so well known elsewhere) with his son Tristan.
[QUOTE=D_Odds]
Rick Wakeman and Adam Wakeman. I also think another son of his is also a rock ‘star’; I want to say Oscar, but I’m not sure.
[/QUOTE]
Oliver.
Pete and Lee Agnew - bass and drums for Nazareth.
[QUOTE=42fish]
Mother/Son
Shirley Jones (The Partidge Family)/Shaun Cassidy
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And of course David Cassidy was in the Partridge Family with Shirley Jones.
There’s the Zappa family. Father Frank and offspring Dweezil and Moon (who dueted with Frank on “Valley Girl”). There’s another sibling, Ahmet or something, but I don’t know if he sings.
I swear I thought I’d read the entire thread. I missed the Zappa family reference though.
Did I miss the Ozzy/Kelly Osbourne mention too?
Albert Hammond and Albert Hammond Jr.
[QUOTE=Imasquare]
Tal Bachman is the son of Randy Bachman from Bachman Turner Overdrive. Tal had a pretty big hit back in the late 90s with She’s So High.
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Make that “back in 2000 with She’s so High.”
[QUOTE=Frank]
Ricky Nelson was, surprisingly, a teen idol who was pretty good. He was one of the kids on Ozzie and Harriet, had a bunch of top 40s, and sang Garden Party, a marvelously sardonic take on fans. I don’t know much about Nelson. 
[/QUOTE]
I too don’t know much about Nelson either, but one Ricky Nelson sony many may be familiar with is Lonesome Town from the soundtrack to Pulp Fiction.
I’m reliably informed that Nancy Sinatra had a relative that was also in the music business.