Oh, this is a good question. I think the first big news story I clearly remember was the Pan-Am/KLM runway collision in Tenerife, March 1977. I was five and a half, and saw it on the news. I remember being scared half to death by the charred wreckage of the planes and the hangar totally filled with coffins. Just the thing a little girl who loved to fly needed to see, huh? Mom and Dad had to explain to me that this wasn't a normal thing in air travel. Besides, when were we ever going to Tenerife? :p
Later that year, Elvis died. The other big story of '77!
The next year, the big story was Jonestown. Now that was a news story I wish my parents had turned the T.V. off for. :( How do you explain mass suicide to a seven-year-old? But Mom and Dad were firm believers in not sheltering me or my sister from the harsh realities of life. The news was always on at dinnertime. Probably why I'm still a news junkie today, and why my guilty pleasure television shows are disaster documentaries.