For me, it would be (in no order):
Football:
2011: JMU, I remember the ODU chants were deafening.
2011: Norfolk State Playoffs, incredible atmosphere, first playoff game and home AND win, and I love the cross-town rivalry. NSU fans/band/cheerleaders were excellent
2012: New Hampshire, because Heinicke
2012: The home game against Delaware when we practically played in a hurricane, even though I ran the "ODU" flags out of order and got threats for the rest of the season lol, being booed by 20,118 people was not fun but the actual game was awesome to be at
2012: Georgia Southern home playoff game even though we lost. It was a roller coaster and probably one of the best atmoshperes at a home game (bar the VT game)
2014: OT win over Louisiana Tech
2018: Beating VT
EDIT: I forgot UMASS 2011. That was the fateful night DeMarco hurt his ankle and a young skinny freshman by the name of Taylor Heinicke saw his first action as ODU's QB :D
Basketball:
2009/2010: Beating VCU at home to stamp our ticket to the tournament, winning the CAA regular season outright, full, packed house with the Monarch Maniacs at their peak, nailbiting game til the end... I not only lost my voice but had a headache for days from the amount of yelling I did lol
2010/2011: Georgetown at home. I had a high school friend who played for Georgetown who shot the game-deciding 3 pointer to end the game (Jason Clark) but we played really well and had a chance to beat them, even til the end
2010/2011: Bracket buster against Cleveland State
2010/2011: I can't remember who it was against BUT THE FREE RAISING CANES GAME the place went wild when Trian hit the 3 haha
2014/2015: Home game against WKU, the atmosphere was incredible
2014/2015: The Trey Freeman buzzer-beater game
2016/2017: Kent Bazemore bobblehead night against VCU. We lost but the atmosphere was amazing. I loved seeing my favorite player as a student get enshrined in the ring of fame, and it was one hell of a game til VCU started to slip away at the end
I'm sure there are more that I can't think of off the top of my head