I watched live coverage of the earthquake, and later tsunami. I turned the television on when my house was still shaking from said earthquake.
In a similar vein, last year I turned the television on to live images of Mount Ontake erupting. I went outside to take a look at the mountain with my own eyes.
I caught the OJ car “chase” live. That was a surreal bit of television.
This was my first thought. It was odd because I normally don’t watch Saturday Night Live.
I was watching a Canadian politics channel many years ago - I don’t know why, I must have been channel-surfing and landed on it - and they were debating a bill. The Member of Parliament (or Provincial Parliament, I don’t remember if it was Federal or Provincial) kept referring to it as a “bully bill.” The next day this “bully bill” outburst was all over the news. I thought it was funny that I had actually watched that debate when I had never watched a debate before or since.
I worked in a large corporation and my work area was right next to an auditorium with state of the art video equipment.
I went into the auditorium just after the second tower was hit. I saw the towers fall on a 35 foot screen.
I’m also an old fart and saw the “one small step for man” on the moon.
I just remembered one I don’t think has been mentioned yet – John Glenn’s orbital flight in Friendship 7. I remember my parents tracing out the path on our globe with thumbtacks and thread.
Most of mine have been mentioned. How about Prince William and Kate’s wedding?
Some already mentioned –
Virtually every Apollo launch and splashdown; “In the beginning…”; “one small step…”
Nixon resigns.
Berlin Wall celebrations
OJ chase and verdict
2nd plane impact
Wardrobe Malfunction
Chilean miner rescue
But also a more obscure one but quite impressive IMO –
Televised address by George HW Bush Sept 27 1991:
Jonathan Edwards breaking the world record triple jump in 1995.
Sinead O’Connor ripping up the photo of Pope John Paul II (“Fight the real enemy!”)
I will confess (red-faced) that I watched Geraldo Riviera’s infamous special about opening up Al Capone’s vault and finding…absolutely nothing.
Not really “live”, but I do remember seeing the “General Hospital” episode in which Luke & Laura got married - my sister was a fan at the time and she and her girlfriends bulldozed into the room, turned off the reruns of “Batman” I was watching and took over the TV set for the next hour. (I think I mostly remember it as the first time I ever saw Elizabeth Taylor in anything.)
The one with the vault from Titanic was even better! 
It was 17:00 in Moscow. I had just finished working on a translation and had to get ready for an open house the language school where I taught was giving that night. I was about to turn off the radio when the BBC World Service announced “We now switch you to New York, where something is happening at the World Trade Center.”
I went into the living room and turned on the TV just in time to see the videotape of the second impact on CNN. I was already on the phone with my ex and said “Oh, God! That was no accident, that was no small plane! That was a kamikaze attack!”
Similarly, I just happened to turn to the South Carolina football game when Marcus Lattimore suffered his horrific leg injury. I remember thinking that I probably just saw that dude’s career end, and that pretty much ended up being the case.
For a couple of years, I did the news for an English-language radio station in Moscow. I learned about all breaking stories either as they came over the wire or popped up on CNN. I was the one who broke both the Oklahoma bombing story and the OJ verdict for those who were listening at the time.
I remember watching one of the Mercury launches; I think it was Glenn’s, because I’m pretty sure the rocket was an Atlas and not a Redstone.
I was not yet 14 when I saw Nixon resign, live. That was just surreal.
(I swear Louis CK looks and acts so much like my brother it’s bizarre! Bro has a bit more hair though.)
The moon landing. I’m not sure some of our younger Dopers are cognizant of what a huge freaking deal that was then.
The first broadcast of MTV. God that channel was great back then!
I saw both Secretariat win the greatest horse race in all of history, and Ruffian in the worst horse racing disaster in history.
Not on TV, but I was listening to a talk station on the radio while driving to work. They announced a fire in the WTC, and that they could see the smoke from the studio. Then word came in that a plane had crashed into the building. Everyone assumed that it was a small private plane that had gone off course, though one newscaster who was a pilot seemed to think that it was something bigger. When they received the news that it was a commercial airliner, and then the second plane hit, panic set in as they realized it was not an accident.
The 1989 World Series Earthquake game.
Sinead OConner Pope thing
Collapse of the WTC
OJ bronco chase
OJ trial
Coverage of OKC bombing
Waco
Rodney King Riots
WTO riots in Seattle
Labor Day riots in Seattle
Mary Lou Retton’s winning performances
Clinton playing Sax on Arsenio
MTV’s first Rock the Vote interview panels with Presidential candidates
Nipplegate
Britney and Madonna’s kiss
Rage Against the Machine’s weird protest at the MTV music awards
Nirvana playing the live perf where Krist Novoselec clocked himself with his Bass
Announcement of Kurt Cobain’s suicide
Wasn’t alive for JFK (or Oswald), wasn’t old enough for Apollo 11 (kinda remember 17), and unfortunately I worked third shift my whole life so I slept thru Challenger, 9/11, and Columbia. Actually I’m sorta glad I wasn’t awake to see 9/11 happen…
Did you catch it on CNN live or watch the replay really soon after? I watched it not-quite-live, but within minutes of it happening.
Me too!
I also remember the moment they announced the name of the Oklahoma City bomber. I can pinpoint the exact moment I first heard the name Timothy McVeigh.