I think a ton depends on whether your team is in it or not.
I'm just gonna list my personal top five + one events I've watched on TV:
1. Mets v Astros, Game 6, 1986. The drama in that thing was ridiculously intense.
2. 77-74 and everything leading up to it.
3. Mets v Red Sox, Game 6, 1986.
4. Ali-Foreman, 1974. Many folks thought Ali would literally be killed.
5. USA v USSR, Lake Placid
6. The current NC run, not because it was dramatic, but because of the level of play. It was the Globetrotters vs the Washington Generals every game.
As for live events, it was the 2013 WC game between the Pirates and Reds. I doubt I'll ever experience anything close to that. I'll understand that this isn't on anyone else's list, living here and watching that Pirates team bring baseball back to Pittsburgh and all that happened early on in that game - couldn't ask for a better experience.