If lottery shows count, the most heartbreaking moment may never even have aired. On California's Big Spin show back in the early days of the state lottery, a contestant spun the wheel (it consists of a ball inside of a wheel that has 100 posts arranged on the front face of the wheel near its edge; eventually, the ball comes to rest between two of the posts, which back then had dollar amounts from $10,000 to $2 million), and as the wheel was slowing down, the ball landed in one of the $2 million slots; the music started playing, balloons and confetti started dropping, the contestant's family came out to celebrate with her - and then the host (I think it was Geoff Edwards) had to announce that "the ball did not stay in the $2 million slot for the required five seconds" (the wheel was still moving and the ball popped out after about 4 1/2 seconds) and eventually landed in a $10,000 space. Back then, there were 20 spinners per week, and the show was only 30 minutes long, so they only aired about half of each week's spinners; presumably, this spin was one of the ones cut from the broadcast.
(Note that, years later, she sued the lottery commission for $2 million and won, in part because she had tapes of other spinners where they did not apply the "five-second rule".)
Here are some others I can think of:
A number of times on the syndicated version of Let's Make A Deal, during the big deal, Monty would reveal one contestant's door, and then open the door nobody chose, to the delight of the other contestant, who thought they had won the Big Deal, only for that second door to have the Big Deal behind it.
A descendant (I don't know if she was a direct descendant or not) and namesake of Susan B. Anthony was on The $128,000 Question and got the last part of the $64,000 question wrong - and then immediately realized what the correct answer was.
Back in the days of the isolation booth and the "$100,000 Mystery Tune" on $100,000 Name That Tune, the contestant and a sizable chunk of the crowd (and myself as well, watching on TV) thought the money was in the bag when the pianist started playing the first song from Guys & Dolls ("I've got the horse right here / The name is Paul Revere / And here's a guy that says if the weather's clear...") and the response was "Can Do" - unfortunately, the actual title is "Fugue for Tinhorns" (although they would have accepted "I've Got the Horse Right Here" as well).
However, the most heartbreaking moments of all are probably the "contestants" on Fox's The Rich List who won hundreds of thousands of dollars finding out that Fox cancelled the show before their episodes aired so they wouldn't be receiving any money. (I thought some of the laws passed after the 1950s scandals prevented this sort of thing.)
-- Don