The best thing I ever witnessed in person might be a tie. On my 13th birthday, Scott Niedermayer scored a hat trick for the New Jersey Devils and they beat the Bruins in OT - that was cool!
However, I think the game that took the cake was when the Yankees played the Devil Rays a few years ago - I think Randy Johnson was starting against Hideo Nomo if I recall correctly. I was visiting my dad in the summer and we wanted to get tickets to a game - he insisted we go to see the "great" Randy Johnson, and we got some great tickets on StubHub, I mean, GREAT tickets (and we moved up too!) and went on a sweet journey to the game that involved a subway ride and almost getting lost
Anyway, Randy Johnson stuck and the Devil Rays pounded on him for like seven runs. Eventually the game really got out of hand and the Yanks were within a few runs by the time the 8th inning rolled around, and then before you know it, the Yanks bats went absolutely apeshit insane and I thought we were watching batting practice. We pitied the people who all left the game because this was a fireworks show - 13 runs in the 8th with several home runs. Posada, Rodriguez, Matsui, and Sheffield I think, all sent ones into the seats. Matsui jacked one into dead center and I think he had a RBI double earlier in the inning.
The best part was Bernie Williams bases-loaded triple that gave the Yanks the lead. I will never forget that one. He smacked it over Damon Hollins head in center field and he had a lot of trouble fielding the ball - if Bernie was younger, it would have been an inside-the-park home run for sure. But the 3 RBIs had capped a few base hits and took the lead, and then the next seven runs were just for show. It was really absurd.
I managed to jack the clip from MLB because I knew eventually they'd take it down or ask money for it,and I'm so glad I did
I will ALWAYS remember Aaron Boone sending a moonshot on the first pitch of the bottom of the 11th in game 7 of the 2003 ALCS to send the Yankees to the world series. It was easily a moment that could have been missed, and the call for it isn't really legendary in its own right but when I just THINK about how he turned on the pitch and sent it into the left field seats I get some serious chills. NO ONE would saw that coming and it was just like a cold nail right into the heart of the Red Sox Nation (who would get their revenge).
That's probably the best moment I've ever witnessed on TV. Clips of a few things mentioned here also give me chills - Gibson knocking Eckersley's pitch out and hobbling around the bases and Vin Sculley's call, Mets v. Red Sox in '86 and the Bill Buckner play (a little roller up along first .. BEHIND THE BAG! IT GETS THROUGH BUCKNER! HERE .... COMES ... KNIGHT AND THE METS WIN!!!!!!!!!!!!!!!!) and a few more. I have a lot of random clips saved of good events like this
Aside from Baseball, I've seen a clip of Dennis Bergkamp scoring one against Argentina to win it for the Netherlands in the final seconds and the announcer completely loses his mind.