Let's see, in chronological order:
1) Challenger explosion, January 28, 1986. It was bad enough seeing what happened live on TV; it was entirely something else to be able to see what looked like the Death Star exploding over my back yard when I was six years old.
2) San Franciso Eathquake, October 17, 1989. The eathquake made the feed cut out for the World Series game in progress; when it came back on, it loked like the Bay Area was in ruins.
3) World Trade Center/Pentagon Attacks, September 11, 2001. Goes without saying. Angry Saudis kill 3000 people, then sit back and laugh as the U.S. descends into madness over the next decade.
Some honorable mentions, and why I didn't include them:
Mt. St. Helens Eruption, May 18, 1980: It happened two weeks or so before I was born, so not technically during my lifetime. Perhaps it was an omen.
Gulf War/Desert Storm, 1990-1991: Heavy U. S. involvement, but technically happened somewhere else.
Ongoing wars in Iraq, Afghanistan, 2001-present: Again, technically it's going on somewhere else.
O.J. Simpson Trial, 1995: Nothing really important in the grand scheme of things, but it was memorable that we in the U.S. had absolutely nothing better to do with our time in 1995 than watch a sports legend go to court.
Oklahoma City Bombing, April 19, 1995: Shh, I'm busy watching the O.J. Simpson trial!