The Munsters, on CBS
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This show is often compared to The Addams Family, as they share a similar theme. However, this was perhaps a bit sillier than that show, and the Munsters were more working-class than the Addamses, and most importantly, they were actually monsters. But like the Addams Family, the Munsters were oblivious to the fact that they were different from anyone else, constantly baffled by people's behavior around them; it never seemed to occur to them that anyone would have any reason to be afraid of them. Anyway, the show was basically an absurd parody of the family sitcoms of the era. The father figure was Herman Munster, who looked like Frankenstein's monster, but he was actually a dopey, good-natured guy who could occasionally be kind of childish. He was married to Lily, who was kind of vampirish. She was smarter and more sensible than Herman, but of course they loved each other and were... well suited to each other. Also living with them was Lily's father, "Grandpa," who was kind of a parody of Count Dracula, with a touch of the mad scientist mixed in, and he didn't always get along with his son-in-law. Herman and Lily also had a young son named Eddie, who was kind of a wolf-boy. Also living with them was their niece, Marilyn, who was a normal and attractive young woman, though her family saw her (and she saw herself) as a freak or monster or ugly duckling or whatever. (It's weird that they never noticed that she, unlike the rest of them, looked like everyone else in the world; that might have served as a clue to why people acted the way they did toward the family, but whatever. It's just a gag, and doesn't bear close analysis. Also I should mention that she was played by two different actresses, with the second one assuming the role in the middle of the first season.) Anyway, that's all I can think to say. It was just a goofy, ridiculous show, but kind of fun.
In 2012, there was an attempted reboot called Mockingbird Lane, but it never made it past the pilot episode, which aired as a Halloween special.