In person I haven't seen anything that was a historic moment per se. The most close is probably July 1, 1973. Hal King hit a three run HR for the Reds in bottom of the 9th to spur a huge comeback for the Reds to win the NL West against the Dodgers. The Reds were 11 1/2 back that day and after that win they got Red hot and won the division.
On TV I have seen most every historic moment in MLB,NFL,NBA,Colleg football & basketball. I watch way too much sports.
The ones that stand out are Hank Aaron 715th HR. Watch that with my dad. It was on Monday Night baseball on NBC.
Evfen though it was hugely disappointing to me (UK Fan),Christain Laetners game winning shot in 92 regionals. One of best games I haver ever seen. Just not the perfect ending for me.
Pete Rose's record breaking hit. I was in college and watched it a dorm lounge with a bunch of others. After Rose got that hit the lounge emptied out and I could watch the rest of the game in peace.