Probably the best game I ever went to was Red Sox Opening Day
in 1998. The Sox were down 7-2 in the bottom of the ninth, and came back to win 9-7 on a grand slam by Mo Vaughn
with no outs. Great game.
I also sat through an entire 16 inning game between the Red Sox and White Sox. Sitting on the third base side, the entire section chanted "Daryl! Daryl!" at Daryl Boston. Then one inning, we forgot to do it, and he stopped before going out to his position and reminded the crowd. Someone from our section hit Ozzie Guillen with a hot dog during one of the extra innings and got thrown out of the game.
I saw a Cubs-Braves game at Wrigley Field in 1998 where Kerry Wood and Greg Maddux battled into extra innings. The Cubs won it in extra innings on a home run.
I also sat in Section 1, Row 1, Seat 1 for a Red Sox game (that's the right field corner). My friend and I took turns sitting in the seat each inning... he got to keep the stub.
I went to a Cleveland Indians game at Fenway Park. The game was called because of rain, but two guys ran out onto the tarp and mooned the crowd. Then they sprinted back to the bleachers. They started climbing up the fence in the bullpen, and the first guy made it over. The second guy was halfway over the fence when a cop grabbed his pant leg. Unfortunately (or maybe fortunately) he hadn't fastened his pants after mooning the crowd, and they came right off, sending the cop flying backwards and the guy tumbling, half-naked, into the crowd. Both guys hauled ass down the concourse to a standing ovation.