Captain Robert Falcon Scott, Antarctic explorer, second to reach the South Pole. Died tragically on the return journey.
His son Sir Peter Scott, ornithologist and conservationist.
Louis Leakey and his son Richard Leakey, both prominent palaeoanthropologists.
OK. Never mind then. I was confused.
She died too soon and was the wrong gender to make the contributions to mathematics that her father did to literature, but Ada Lovelace and Lord Byron would probably fit here otherwise.
I thought of another candidate:
John B. Sebastian (Lovin’ Spoonful, etc.). Among his other talents, JB Sebastian is a harmonica virtuoso.
- YouTube
His father, John Sebastian, was a classical harmonica virtuoso.
*- John Sebastian Plays Bach, LP,Columbia Special Products P 14210
John Sebastian Sr & JR:
Neat family resemblance
Senior:
*http://www.google.com/imgres?q=john+sebastian+harmonica&hl=en&newwindow=1&safe=off&tbm=isch&tbnid=FglHT0C5i6GbXM:&imgrefurl=http://www.vintageadbrowser.com/music-ads-1940s/7&docid=gcFrU0TPxElrFM&imgurl=http://file.vintageadbrowser.com/l-ico9yhpkvt8qcn.jpg&w=660&h=924&ei=8_LsT8SMKoe6rQGys7GADg&zoom=1&iact=hc&vpx=615&vpy=117&dur=5721&hovh=266&hovw=190&tx=99&ty=127&sig=101875493425199486898&page=1&tbnh=142&tbnw=128&start=0&ndsp=17&ved=1t:429,r:3,s:0,i:84&biw=1024&bih=675
*
Junior:
http://www.johnbsebastian.com/bio.html
The Bach’s don’t count. 
I nominate Martin Luther and Martin Luther King Jr. 
Ha! I knew it would get your attention. Believe it or not, our recent micro-debate isn’t what made me think of the two JS’s. Pure coincidence.
Of course, realizing it might make your nostrils flare for just a moment there…put an irritating smirk on my face.
By the way- what’s your favorite CPE Bach composition for solo keyboard?
Phillida Law is a wonderful character actress who’s played skillions of quirky or charming rolls beautifully. Her daughters are Emma Thompson and Sophie Thompson. Emma-- well, we all know Emma. Sophie is marvelous too, particularly as a comic actress (she and her mom played the sweet, funny Miss and Mrs. Bates in the Paltrow Emma).
Rosemary Harris is an extremely gifted stage and film actress who’s been nominated for an Oscar and a BAFTA, and has won an Emmy, Tony, Obie, and Golden Globe Award, as well as five Drama Desk Awards. Her daughter is Jennifer Ehle–not yet as lauded, but the adoring following of the 1995 Pride and Prejudice, in which she was a luminous, intelligent, funny and touching Eliza Bennet, will probably agree she’s no slouch either. Oh, and I should mention Harris’s husband/Ehle’s dad is John Ehle, a highly-esteemed Southern writer who according to Wikipedia is a member of the NC Hall of Fame, with a Thomas Wolfe Prize, the Lillian Smith Book Award, the John Tyler Caldwell Award for the Humanities, and the Mayflower Award.
Robert Earl Jones was part of the Harlem Renaissance and worked consistently and with critical acclaim in the theater, films (particularly The Sting as Luther Coleman) and TV. His son is James Earl Jones, 'nuff said.
ok, per your criteria here are additions to that list.
Scott Caan
Ben Stiller
Sigourney Weaver
Mia Farrow
the Deschanel’s
Kate Hudson
Nick Cage (yes, that Uncle counts)
Melanie Griffith
Jeff and Beau Bridges
Allison Eastwood
Katherine Houghton (yes, that Aunt counts)
the Kardashian’s <ahem!>
Angelica Huston
Bonnie Rait
Laura Dern
Rumer Willis
Tori Spelling
Geraldine Chaplin
Christian Slater
the Gyllenhaal’s
Keira Knightly
the Fonda’s
Vincent Cassel
Tim Robbins
Daniel Day-Lewis
Isabella Rossellini
Minka Kelly
Rob Reiner
Sean Penn
Helen Hunt
Mariska Hargitay
George Clooney
Alan Alda
Pauly Shore
I am getting bored with this now…
good bye.
Natasha Richardson had some pretty acclaimed parents, Tony Richardson and Vanessa Redgrave. Since she played Mary Shelley once, she seems appropriate to include.
Minnie Riperton==>Maya Rudolph
Eric Roberts==>Emma Roberts. I think they’re both enormously talented.
Lucky, as opposed to “enormously talented”…
I’d add:
Frank Zappa’s kids
Gary Lewis (son of Jerry)
Joachim Cooder
A study of military history will also reveal various famed military officers who had some danged noteworthy offspring. Teddy Roosevelt’s eldest son, Theodore Roosevelt, Jr., fought in both World Wars and received the Medal of Honor for his actions leading troops ashore at Utah Beach as a Brigadier General (he died a month later of a heart attack, in his late 50’s)
Commodore Stephen Decatur, Jr, famed for his actions during the Quasi-War, the Barbary Wars, and the War of 1812, was the son of Commodore Stephen Decatur, Sr, a naval officer during the American Revolution. That said, the senior Decatur isn’t all that famous.
Major General Robert Olds served as a fighter pilot in World War I, and would later be one of the men responsible for developing the American daylight precision bombing strategy that would be used in World War II. He also had a major role in establishing Air Corps Ferrying Command, which would be responsible for delivering newly built planes to the front lines all over the world in WWII.
His son, considerably more well-known today, was Brigadier General Robin Olds, a triple-ace who fought in WWII and the Vietnam War.
To add on to the list, there is Benjamin O. Davis, Sr, first African American general officer in the Army, and his son, Benjamin O. Davis, Jr, first African American general officer in the Air Force.
Another example from the military is Arthur MacArthur, Jr., lieutenant general in the US Army and winner of the Medal of Honor and his son, Douglas MacArthur, a five-star general and also winner of the Medal of Honor.
pointing out that the question in the OP is pretty much unanswerable is not really a ‘nitpick’, IMHO 
Father and son Medal of Honor winners - Arthur MacArthur and Douglas MacArthur, Theodore Roosevelt SR and Jr. In sports Ken Griffey SR and jr, Dale Earnhardt and son, Joe Jellybean Bryant and Kobe, Doc Rivers and Austin, and dare I say Bill Walton and Luke? OK so maybe Luke isn’t really all that successful, but he made it to the NBA, and he can sort of do a victory dance.
Francis Ford Coppola had an Academy Award-winning writer and nominated director. Not the same / as good as he but still a very good achievement for an American female director.
? I guess you hate Nicholas Cage.
Anyway -
Surprised no one said John/Julian Lennon. Jr isn’t on par with his dad but he IMO is very talented and did some very good stuff.
No clue who Kinky Friedman is, but obviously he/she is tone deaf. Jr is an alcoholic moron with about as much musical talent as Tiny Tim.
You know that Cage is Coppola’s nephew, not son, right?
I like lots of Cage’s stuff, but wouldn’t put him in the A-league with De Niro and Hanks.
