the series that made them well-known ended its network run.Cases in point:1)John Astin.After "The Addams Family" ended on ABC in 1966,his career did NOT die.He did NBC's "Hey,Landlord",CBS'"Gunsmoke",CBS'"The Wild Wild West",NBC's "Bonanza",ABC's "The Flying Nun",in the 1960's ,did movies like 1966's "The Spirit is Willing",(an "The Addams Family"-esque-comedy in which he played a psychiatrist),1968's"Candy",and 1969's "Viva Max",directed some ,co-starred in the 1970's "The Doris Day Show"(in an episode when she was a widow)NBC's "Night Gallery "(he also directed several episodes),ABC's "Welcome Back Kotter"the series "Operation:Petticoat(the first season only),"and again playing Gomez Addams in NBC's "Halloween With the Addams Family",and as Buddy in NBC's "Night Court",and his memorable performance in NBC's "Mad about You".And in the 1990's,played the voice of Gomez(who else)on ABC's cartoon version of "The Addams Family"(for which he won an Emmy).Now he's probably retired,and is an acting teacher.Getting back to the original question:Know of any other actors/actresses whose career did NOT die when the series that made them famous ended?

Actually, I can think of several examples:

Andy Griffith (from The Andy Griffith Show to Matlock)
Dick Van Dyke (from The Dick Van Dyke Show to Diagnosis Murder)
Michael Landon (from Bonanza to Little House on the Prairie)
Ron Howard (from The Andy Griffith Show to Happy Days)
Gene Barry (from Bat Masterson to Burke's Law)

Just to name a few.

Tom Hanks - Bosom Buddies to the big screen.
Beatrice Arthur - Maude to the Golden Girls.
Betty White - Mary Tyler Moore to The Golden Girls
Katherine Helmond - Soap to Who's the boss.
Billy Crystal - Soap to the big screen.
Tony Danza - Taxi to Who's the boss?

Courteney Cox from Family Ties to Friends to Cougar town
Matthew Perry Friends to Mr Sunshine
Ed O Neil Married with Children to Modern Family
Katey Sagal from MWC to Sons of Anarchy
Neil Patrick Harris from Doogie to How I met your Mother
Tom Selleck from Magnum to Blue Bloods
Allyson Hanigan from Buffy to How I Met Your Mother
Sean Hayes from Will and grace to Broadway
Willie Garson from Sex and the City to White Collar
Andrea Anders from Joey to Better Off Ted to Mr Sunshine
Allison Janney from West Wing to Mr Sunshine
Chris Noth from Law and Order to SOTC to the Good Wife
Paolo Constanza from Joey to Royal Pains
Jane Leeves from Frazier to Hot in Cleveland

Actually, I can think of several examples:

Andy Griffith (from The Andy Griffith Show to Matlock)
Dick Van Dyke (from The Dick Van Dyke Show to Diagnosis Murder)
Michael Landon (from Bonanza to Little House on the Prairie)
Ron Howard (from The Andy Griffith Show to Happy Days)
Gene Barry (from Bat Masterson to Burke's Law)

Just to name a few.
Also, Ron Howard went from Happy Days to one of the most major movie directors in the business!

And,John Travolta ,when he walked away from "Welcome Back,Kotter",sang some-Solo:Remember the 1976 song "Let Her In?"(#10)-sang with Olivia Newton-John and starred with her in the mega-hit movies "Grease",did the film "Saturday Night Fever",and "Urban Cowboy",both smash hits,and other smash hit films.

Allyson Hanigan from Buffy to How I Met Your Mother...i cant forget her

Kim Fields- After The Facts of Life ended she went on to star in another successful long running sitcom called Living Single. She is also a director of tv shows such as Taina, Living Single, some Tyler Perry sitcoms, Kenan & Kel. She just wrapped up a season on the successful reality show Real Housewives of Atlanta and she is now doing really well on Dancing With The Stars.

Nancy Mckeon- After The Facts of Life ended she went on to star in several successful made-for-tv movies. She also starred in a good show called The Division.

Jennifer Aniston from Friends to lots and lots of movies. You could say that her role on Friends is what got her recognized.

Will Smith from Fresh Prince to lots and lots of movies.