I was too young to have watched/remember anything before 2000. With that said, I know the stories. 98 MSU in particular is pretty mind-boggling. Not only would OSU have been National Champions if not for that loss, but they would have been #1 from preseason through bowl season, which has only happened a couple times in the history of the sport.
Going way back, 1979, Earl Bruce's first season. OSU was undefeated and #1 and lost the Rose Bowl to #3 USC by 1 point. USC took the lead with under 2 minutes left. That's pretty rough.
Anyway, for games in this millennium, there's a few that will always stand out to me:
1) 2022 Georgia. Touched on it in the main thread, but if literally anything goes our way in the 4th Quarter, we win the game and go on to beat TCU in the National Championship.
2) 2019 Clemson. Also touched on it in the main thread, but this was a combo of self-inflicted mistakes and getting royally fucked by the replay booth. This game robbed us (and everyone) of what would have been an epic National Championship Game against Joe Burrow and LSU.
3) 2005 Texas. Man, OSU really beat the shit out of themselves in this one. Shuffling QBs, terrible red zone execution, Ryan Hamby...this game (likely) cost en elite OSU team a chance to play USC in the National Championship Game.
4) 2013 MSU. OSU had a flawed team this year, but their running game was basically impossible to stop and this game cost them an appearance in the National Championship Game against what would have been a heavily-favored Florida State team led by Jameis Winston.
5) 2015 MSU. This one might be higher on the list for some people, but if I'm being honest, this entire season was a shitshow from the very beginning. The coaches failed this team all season long, and it felt inevitable that a loss was coming at some point. If it wasn't this nightmare of a game, it would have been in the Playoff. With that said, for this team to have not even made the Playoff and get that opportunity is pretty mindblowing given the talent they had.