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Felix and Oscar, "The Odd Couple" (1970-75)
Why They Worked: Based on the movie of the same name, which itself was based on the 1965 Neil Simon play, The Odd Couple had Felix (Tony Randall) neat and high-strung, while Oscar (Jack Klugman) was a sloppy, sports-obsessed guy's guy. But as divorced guys in the early '70s, that was enough to tolerate one another as roommates.
Why They Were Odd: Why they were ever friends in the first place is hard to grasp, but it made for classic comedy.
What Made Them Memorable: Excellent writing and spot-on acting, really.