This is a good topic. I have a few. And, more will come to mind in the future. Then I'd have to compare to figure out which is earliest. As of now, I remember the 1972 Munich massacre; I remember the Dolphins perfect season, but that was later in 1972. I think I also may remember the year before too, when they lost to the Cowboys in the big game. If not, subconsciously, it is still the root of my disdain for the Cowboys franchise. I'll have to edit when I think of more.
***WARP, I've heard all the stories of the NY "Jints" as my grandfather called them. Despite eventually moving to Brooklyn, he was a lifetime diehard fan. (even after the move). And, if anyone has not seen the Polo Grounds, go online and find some old photos. It's incredible that they played baseball there!