But I'll just break it down to the most tense...
1997 Game Six WCF between the Utah Jazz and Houston Rockets.
Backstory: The Jazz had been the most successful Western Conference team to never make the NBA Finals. Year in and year out they'd get to the conference finals and lose. Either to the Blazers (1992), Rockets (1994) or Sonics (1996). Finally, in 1997, they held home court!
After going up 2-0, the Rockets tied the series 2-2 and Utah won Game Five in Salt Lake to send it back to Houston for Game Six.
The Jazz weren't favorites to win and most believed the series would head back to Salt Lake for a Game Seven.
After Utah fell behind by nearly double digits with two minutes left, it looked as if that would happen. Then John Stockton stepped up and put the Jazz on his shoulders. He scored...and scored...and passed...and scored.
The Jazz quickly erased the lead and the game was tied with 2.8 seconds left. Utah had the ball. Russell inbounded, found Stockton - who was wide open - and he sank the three at the buzzer.
Jazz win! Jazz win! They advanced to the NBA Finals for the first time in franchise history. Though they'd lose to the Bulls, it was the most tense moment of my life. I nearly passed out waiting for them to inbound that goddamn ball. Then when the shot was made...I nearly keeled over in happiness.
http://www.youtube.com/watch?v=Qobv8yUTJ_EI still get teary eyed when I watch that!
2) 2009 Sugar Bowl.
I was a nervous wreck prior to it. The Utes weren't picked to win and many felt they'd lose in a blowout. However, they jumped on the Alabama Crimson Tide 21-0 and looked to cruise. The second half, though, started out horribly for Utah. They fumbled on their first possession and two plays later, the Tide scored a TD to get back into the game.
The rest of the second half was Utah pulling away before eventually winning.
But damn, that was a tense game. Greatest win in school history, but tense as hell.
3) Game Six 1998 NBA Finals.
This was an elimination game for the Jazz and they lost. But it was back and forth and probably one of the greatest Finals games in NBA history (it's the one where Jordan pushes off for his final shot).
I hated the outcome, but certainly one of the most tense moments ever.
There you go. I have tons more, but I won't list 'em.