Til Death Do Us Part is a British Show that inspired the US show All In the Family, Which spun off The Jeffersons which gave us Checking In, Gloria, 704 Houser Street, Archie Bunker's Place and Maude which Gave us the Good Times
Some of these US shows were made into British versions such as Good Times into The Fosters and Maude into Nobody's Perfect.
Mary Tyler Moore's spinoff Rhoda gave us a spinoff primetime animated special starring the doorman called Carlton, Your Doorman and there was the Mary and Rhoda telefilm.
Golden Girls, Golden Palace, Empty Nest and Nurses.
Doctor Who (original), Doctor Who (current), Torchwood, Sarah Jane Adventures and K-9 & Company.
Below, about Happy Days, aside from Mork & Mindy, Joanie Loves Chachi and Mork & Mindy, there are more now that I think of it, including Blansky's Beauties, Fonz and the Happy Days Gang (animated), Laverne & Shirley in the Army (animated), Mork & Mindy (animated) and Laverne & Shirley in the Army with the Fonz. Also, Love American Style spunoff Wait Till your Father Gets Home.
In a similar vein of spinoff of anthologies, the British Comedy Playhouse gave us Are You Being Served which gave us Grace & favour and the Australian Are you Being Served which had John Inman of the original being lent out to Mr. Grace's cousin and the US version Beanes of Boston with Charlotte Rae, John Hillerman and Alan Seuss. Also from this series is Steptoe & Son which inspired the US Sanford & Son which spun off Grady, The Sanford Arms, and Sanford. Other series from this include Last of the Summer Wine, The Liver Birds, and All Gas and Gaiters. This also gave the series Till Death Do Us Part which inspired All in the Family above which brings us full circle.
Comedy Playhouse in my mind is the winner.