You just want something that occurred between 1950 and 1990 that not everyone knows about? You're not going to narrow it down at all? No particular regions you're interested in? Do you want to write about a conflict? A particular type of event?
There's the 1970 FLQ Crisis [http://en.wikipedia.org/wiki/FLQ_Crisis], in which a group of militant French-Canadians kidnapped some politicians, which led to invocation of the War Measures Act and the dramatic temporary expansion of police powers.
In 1976, Israeli commandos staged Operation Entebbe [http://en.wikipedia.org/wiki/Operation_Entebbe], in which they went to a Ugandan airport where some terrorists had landed a hijacked airplane and were keeping the hostages, killed the hijackers and some Ugandan troops, and airlifted the hostages to safety.
There is also, of course, the 1986 Chernobyl disaster [http://en.wikipedia.org/wiki/Chernobyl_disaster], which is more well-known to your average American high school student than the other two suggestions, but also pretty interesting. A lesser-known but similar incident is the 1957 Kyshtym disaster [http://en.wikipedia.org/wiki/Kyshtym_disaster].
Are these along the lines of what you're looking for?