For me, it was during the 1970 World Series when Elrod Hendricks made a tag of Bernie Carbo at home, with the umpire calling Carbo out. The ump had his back to the plate, and Hendricks had the ball in his bare hand, not in the mitt, which is what tagged Carbo "out." Anyone else remember that?
That was the first time I recall an ump really blowing a call that mattered to me.
What's yours?