I have a lot of these, and some are painful. One that still hurts was a ticky tack call that fouled out Keith "Mister" Jennings where ETSU was poised to be the first 16 to beat a 1 (Oklahoma with Mookie Blaylock and Stacy King.)
In terms of the most exciting moment (where I didn't have a stake), I still remember seeing this live in my 8th grade algebra 1 class (thanks Mr. Fleenor.)
I also watched the Duke Kentucky game with the Laettner shot. I didn't like either team, but Jamal Mashburn had a ridiculous game to keep Kentucky in position to win. I felt ill when Laettner made that shot.
My underdog pick will always be my favorite first round game. Two friends of mine and I from EHC went to the Damons in Bristol VA (RIP) for the first round in 1999. We were there almost 7 hours, and the last game of the night was UNC vs Weber State. Harold the Show Arceneaux put on a show for the ages, and Weber State won the game. We were going crazy in an empty Damons late at night while the poor staff were desperate to go home. (If you worked at Damons in Bristol VA in 1999, sorry.)