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The Thompsons Richard, Linda, and Teddy. Richard and Linda were great as a duo in the '70’s. Lately, Linda has released some great solo work. Teddy has firmly established himself apart from his parents. Richard Thompson is my favorite artist and can’t do anything wrong, IMO.
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The Williamses The Hanks and Holly, too. Hank, Sr. was a songwriting genius, although his voice is an acquired taste. Hank, Jr. is overly criticized because he is not his dad. Hank III is trying to be his granddad reincarnate and not doing badly. Holly is the wink link as she is a Lillith Fair wannabe.
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The Carter-Cashes The Carter Family. Mother Maybelle was a guitar goddess. June Carter wasn’t bad. Johnny Cash is a legend. June had Carlene and Johnny had Roseanne. Carlene’s ex-husband is the great Nick Lowe. Roseanne’s ex-husband is the singer-songwriter, Rodney Crowell. With that pedigree, I wonder why the next generation didn’t get into the family business.
I have to say Rosanne Cash is BRILLIANT. She is even better than her father. Her CD “Interiors” is so eeriely good you’ll have bad dreams after listening to it.
I don’t know how many have to be in a family but Judy Garland / Minnelli are good, and while they have excellent voices, I tend to think of both of them as actresses who sing well, rather than singers first.
Are you looking for families or generations, cause there were a lot of good sister acts in the 50s and before, such as the Andrews Sisters and the McGuire Sisters etc etc…
Either/or
The Wainright bunch – Loudon III, Rufus, Lucy, Martha.
Let’s not forget the Marleys – Bob, Rita, Cedella, Ziggy, Damian, Ky-Mani, Julian, Stephen, geez am I missing any?
Don’t forget the other half of the Wainwright bunch: Kate (Rufus and Martha’s mother) and Anna McGarrigle.
Oh, and the Bachs are pretty famous, too. And not just Johann Sebastian and a couple of his kids. The Bach family was important in German music for almost 2 centuries.
Would Gladys Knight & the Pips count? (Brother, sister, 2 cousins.) If so, they’d be my number 3.
Pointer Sisters 2.
Carter-Cash (in that order).
Not to mention the Roches, who are related somehow to that bunch.
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Ah, my steprelatives the Taylors–Alex, James, Kate, Livingston & Hugh. And James’s ex-wife & in-law’s the Simons–Carly, Lucy & Joanna
There’s the Baez’s, Joan and younger sister Mimi and Mimi’s late husband Richard Farina.
And of course the Brothers Lloyd Webber–Andrew & Julian.
Lucy Wainwright’s mother is Suzzy Roche.
And how about all those Strausses?
There’s also Sloan Wainwright, Loudon Wainwright III’s sister.
jayjay mentioned the McGarrigle sisters earlier.
Loudon Wainwright III divorced Kate McGarrigle (mother to Rufus and Martha) and married Suzzy (pronounced like “fuzzy”) Roche, sister to Maggie and Terre and one of the The Roches. Their daughter is Lucy Wainwright Roche.
Ack, on preview, jayjay beat me to it.
The Beach Boys, brothers Brian, Dennis & Carl Wilson and cousin Mike Love. The Wilson brother’s marriages included:
Brian to Marilyn Rovell, who was a member of the Honeys. That marriage produced daughters Carnie & Wendy, two-thirds of the group Wilson Phillips.
Dennis to Karen Lamm, who had been married to Robert Lamm, founding member of Chicago. Also had a long time relationship with Christie McVie of Fleetwood Mac.
Carl to Anne Hinsche, sister of Billy Hinsche of Dino, Desi & Billy fame, then to Gina Martin, Dean Martin’s daughter & Dino Martin’s sister.
Paul and Mike McCartney*.
Ray and Dave Davies.
The Cowsills. 
George and Ira Gershwin.
*Stage name: Mike McGear
Derek, Ray, and Phil Shulman of Gentle Giant.
There’s also Tim and Jeff Buckley.
All these folks are related and are, or once were, part of the Irish group Clannad:
Members:
Máire Ní Bhraonáin (now known as Moya Brennan)
Ciarán Ó Braonáin
Noel Ó Dúgáin
Pádraig Ó Dúgáin
Former members:
Brídín Brennan
Eithne Ní Bhraonáin (now known as Enya)
Pól Ó Braonáin
Digging into Irish music, we could be here for months.
Oh, and The Boswell Sisters! They’re not very well known nowadays, but they’re fantastic and they inspired the Andrews Sisters.
The Allman Brothers started out with the two brothers (Duane and Gregg) but now have a nephew/uncle in the band with Duane and Butch Trucks. Gregg’s son Devon has a band called Honeytribe. Berry Oakley’s son Berry, Jr. did an album called Bloodline with Erin Davis (Miles’ son) and Waylon Krieger (Robby’s son). (Their other guitarist was the then unknown “Smokin” Joe Bonamassa.)
Edgar and Johnny Winter are brothers.
Angus and Malcolm Young (AC/DC) are brothers. (Right?)
Victor Wooten and Future Man (Bela Fleck and the Flecktones) are brothers. I think there are some other musician Wooten’s as well, but I’m not certain.
All three Los Lonely Boys are brothers.
Carlos Santana’s brother is Jorge Santana. They and their nephew Carlos Hernandez did an album together, Santana Brothers. Jorge was also in the band Malo back in the day. Carlos’ son, Salvador, is on the road with his band opening for Santana now.
Has anyone mentioned the Marsalis family? Or the Neville’s?
And let us not forget the Ramones. Or the Doobie Brothers. Or the Family Stone. 
There’s also that other Irish group The Corrs.
No love for the Osmonds?