My favorite moment was the first game i attended. They lost, but I finally got to see them live. nothing compares to that!
Gotta disagree depending on what game was your first...first game for me was the '93 BC game. Yeah, I might be cursed.
Some favorite ND moment may be when we beat SC in '05, clock runs down to 0, people rush the field...and the PAC 10 blows multiple calls to give the game to the Trojans. If you sat through that game, it was unthinkable to see in person all the BS that occurred in those final minutes. Worst part may be that the game is now vacated, it might as well of gone to us to begin with.
Rocket's kick returns against Michigan in '89
Tate's TD jump into the MSU band
The Bus and the Snow Bowl
Anytime Zibby had the ball in his hands, but specifically the Punt Return and Pick 6 against Tennesee, and the return against USC in '05.
My favorite Zibby moment may be one of the first big games he had. Against MSU in 2004 he pulled the ball cleanly out of a running back's hands, didn't even knock it out, then ran it back for an easy TD. It was hilarious, especially watching their QB stand there dumbfounded for a few seconds. Link is here, at the 5:20 mark:
2004: Notre Dame vs. Michigan State - YouTube
[EDIT] I almost forgot about the 2008 Michigan game! It was pouring down rain like I've never seen at Notre Dame, and Michigan couldn't hold onto the ball to save their lives. I was soaked, but the game was so much fun I didn't care:
Introducing, Your 2008 Michigan Wolverines! - YouTube