Excellent question… my responses come in several categories:
Actual news events:
My primary images of 9/11 are not really the TV images, because I first heard about it on the car radio while driving to work, at which time both the towers had already fallen. So I went into work, and we just hung around watching TV for several hours and then left, but my strongest memory is the sense of shock and national community, not any particular TV image. I didn’t have a TV at the time of Challenger, was never very interested in OJ, and associate the first gulf war more with car radio than TV, and the second more with constantly checking cnn.com.
Actually, the news event that I most strongly associate in my mind with just sitting watching things develop on TV was the death of Princess Di.
Sports:
Far and away the most exciting sports moment that I’ve seen live on TV was the gold medal game in women’s soccer in the 2000 olympics. The US, favored to beat Sweden, went up 1-0 with apparent ease, then gave up two cheap goals, trailed 2-1 going into penalty time, and then, 2+minutes into penalty time, when all hope had failed, SCORED A GOOOOOOOAAAAAAAAAAL!!! (The US went on to lose in overtime, but oh my lord was that goal exciting).
TV Shows:
Many moments from My So Called Life struck strong chords with me, in particular, the ends of Other People’s Mothers, The Life of Brian, and In Dreams Begin Responsibilities, plus the whole scene in the church from So-called Angels.
My favorite TV show, The Simpsons, has provided many memorable moments, perhaps the single most defining being the first time I saw the monorail song from Marge Vs. The Monorail.
Late Night with Conan O’Brien had a sketch a few years ago in which Arafat and Sharon are arguing about the middle east, and GWB and Ozzie Osbourne come in to mediate. It includes Arafat complaining that while trapped in his office, all he had to eat was Bugles and Fluffernutter. I’ve searched hard to find that skit online somewhere, but with no success…
My single most memorable Saturday Night Live moment was on the Andrew Dice Clay show, the brief “Skit Glorifying Hitler”, with Dana Carvey doing an odd by hysterical mishmash of a Hitler impression along with all of his SNL catchphrases.
And finally, the single most stunning thing I’ve ever seen on TV was Cassius’s self-righting mechanism on season 2 (I think… maybe season 3) of the British RobotWars. (The reason this was so stunning was that it introduced an entirely new and unexpected capability to these robots, which we had watched compete for so long… it was more or less equivalent to a human athlete suddenly learning to fly in the middle of a game…)