In addition to all answers provided above, I'd pick the original Sale of the Century. I've only seen a short clip of an episode during the couples format later in its run, but outside a couple UK episodes that had a similar format, it's all gone outside a couple surviving episodes deep in UCLA's vault. Unlike the more familiar versions, a contestant could buy multiple prizes in the Shopping Round instead of just one upon retiring, and progressively higher values for answering a question was a good format of itself, and you still had the instant bargains. But the odds of any of these episodes turning up are almost as long as winning billion-dollar lottery jackpots.
But since we're out in left field, we may as well include non-game shows.
Non-game show answer: The Tonight Show prior to its move to Burbank in May 1972. That's 18 years of interviews, monologues, performances, and skits that would be apt to reveal so much that given how residually popular the surviving Carson shows are. Yet just a few dozen survive in full or in part, mainly because TV wasn't yet seen as a serious enough medium to be worth preserving, and this is surprising since kinescopes could had easily been preserved. In addition to Johnny, I would have loved to see how Jack Paar and Steve Allen enjoyed their tenures.
Children's TV answer: Captain Kangaroo. Before Sesame Street, this was the show that preschoolers would grow up fondly, and only a single episode from the 1960s exist, along with a few from the '70s and early '80s.
Music program answer: 1950s and '60s American Bandstand episodes. Sure, a number of music programs from those decades (especially post-move to Los Angeles in 1963) exist showing the numerous pop/rock/jazz stars of those eras, but American Bandstand always stood out with Dick Clark, rate-a-record, the everyday people dancing around, and of course, the artist interviews/performances. A handful of episodes from the ABC era survive, but only a small amount like The Match Game and '70s Pyramid, but the first five years on WFIL in Philadelphia are all history.