Spitting Image. In the 1980s the puppet-based satire show was the most important topical comedy show in Britain. Now it's almost totally forgotten except as a relic of The Eighties. However, its writers and voice actors went on to do things like Red Dwarf and Blackadder. Some of us, however still see those puppets in our nightmares.
In France, Le Bébête Show went the exact same way, except that their puppets were based upon Jim Henson's Muppet Show. Lasted for ten years or so, before being declared too lame to live, especially because of the comparison between them and their concurrent Les Guignols de l'info, which rose a few years ago on another network.
Les Guignols itself started in the beginning of the nineties, following the very same concept of Spitting Image, and is still aired. Slowly dying of flanderization after the successive departures of Benoît Delépine and, some years after, Bruno Gaccio, who both were a LOT sharper in their writing.
DC Follies, an American show based on the same idea.