Masterpiece Theatre, on PBS
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I never watched a lot of this, I suppose, but I've always thought of it fondly. It basically consists of TV movies and miniseries (or more accurately, limited series), imported from British channels like the BBC and ITV, but there were some American things too. Of course, it started in 1971, which is before my time. I remember it being hosted by Alistair Cooke, originally (and I remember Cookie Monster doing a Monsterpiece Theatre parody on Sesame Street, when I was a kid). Later it was hosted by Russell Baker, from 1992 to 2004. It had no host from then til 2008, when it changed its name to just "Masterpiece," or actually I guess it's split into "Masterpiece Classic," "Masterpiece Contemporary" and "Masterpiece Mystery!" (each with its own host), though I'll always think of it as "Masterpiece Theatre." (And I guess at some point, "Masterpiece Contemporary" was dropped, and "Masterpiece Classic" became simply "Masterpiece.")

Mystery!, on PBS
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This began in 1980... still before my time (not that I wasn't alive, I just didn't watch prime time TV when I was five). Like Masterpiece, I never watched it consistently, but I also think of it fondly. I remember it being hosted by Diana Rigg, though she wasn't the first host (the others were before I ever started watching). I also always enjoyed the opening credits (which have changed, now, alas). Again, mostly imports British TV movies and limited series, and a few regular series (though the seasons of those would be short, by American standards). There have also been a few "American Mystery!" specials. Anyway, the show had no host from 2004 til I guess 2008, when it was absorbed into "Masterpiece Mystery!" (though "Masterpiece" itself continues to have other programs of its own). It's now hosted by Alan Cumming.