Kennedy assassination
Marilyn Monroe dies
I don't think my parents really ever overdid the current events.
Edit: Come to think of it I do remember the challenger accident being discussed at length. Not necessarily by them, but definitely the first media storm I can recall.
For me actively seeking out news:
1988 - Ben Johnson olympic scandal
Mine was when Pepsi overtook Coca-Cola in the stock market, Holy jumpin jeebus
Khrushchev banging his shoe on the table at the UN telling the world he would bury the US. Gary Powers U-2 Spy plane getting shot down over Russia.
I have vague memories of Gerald Ford nearly being assassinated by one of the Manson Family bitches. I didn't notice very much Canadian news until I began to realize how much my parents genuinely hated Trudeau. It was awesome.