You can use multiple shots in one game (maybe the 2007 NCG?) or spread the butter.
I don't want to steal all the obvious ones from the Matta era before others can jump in, so I'll restrict mine to all land pre-2000.
1. 1961 NCG vs. Cincinnati. My emotions and recency bias want to put the next one atop the list, but I can't imagine there should be anything else at number 1... I'd give the first to the #1-ranked 1961 Ohio State team in regulation of the NCG against #2 Cincinnati to give OSU a second (and back-to-back) national title, but more importantly, a perfect 28-0 season, to cement them as arguably the greatest team in NCAA history.
2. 1992 Elite 8 vs. Michigan. The Fab Five still would have had their polarizing (in my case, hated..) place in history with a vacated Final Four run in 1993, but 1992 would have been the year Jim Jackson and the #1 seed Buckeyes owned them in a 3-0 sweep and hung a Final Four banner to go with the outright Big Ten title that year. I think OSU would have handled Cincinnati in the semifinal and run short against Duke, but it still would have made for an amazing season between the Big Ten title, a Final Four, and tournament wins over Michigan and potentially Cincinnati.
3. 1963 regular season finale at Indiana. OSU had just made 3 straight NCGs and just needed a win at IU in the final game of the season to make a 4th straight NCAA tournament. A loss would send Illinois via tie-breaker. OSU lost by 2 in OT that year, ending their season. I'd give them a basket in regulation to punch their ticket.
4. In 1964, OSU found themselves in the same position in the year prior, needing a win in the final game to punch a ticket to the dance or the tie-breaker would go to rival Michigan. OSU lost by 1 at home in the finale to MSU and Michigan sent arguably their best team ever to the dance. I'd give OSU a 2-pointer to punch the ticket and send Michigan home.
5. 1971 Elite 8 vs. Western Kentucky. An OT loss kept the Buckeyes from the Final Four. I'll give Fred Taylor one more Final Four for the rafters.
Two of my 5 cover Elite Eight games, but OSU stands at an amazing 11-4 in the Elite 8 and it's amazing to think our losses have come: twice in OT, once by just 1 point, and once by just 4 points. Put the Buckeyes past the Sweet 16 and we're a Final Four-seeking missile!
Honorable mentions:
1946 - OSU lost to UNC in the Final Four in OT. Another basket has us playing for a NC.
1945 - OSU lost to NYU in the Final Four in OT. Another basket has us playing for a NC.
1950 - OSU lost to CCNY by just 1 point in the Elite 8. Another basket and we're in the Final Four.
1972 - I firmly believe the Minnesota Gophers' season should have been shut down after the assault on our team in one of the saddest chapters in the history of NCAA sports. After starting 13-1 on the season but having players hospitalized as a result of that night, we lost our next contest to a bad Michigan team and finished just 6-4 down the stretch, allowing Minnesota to take the Big Ten title by 1 game. Had we won any of those (a 64-62 loss at Illinois being the closest), OSU wins the Big Ten and the tie-breaker and makes the dance...more importantly, keeping the Gophers from dancing. January 25, 1972 was essentially the night that ended our wonderful success under Fred Taylor as he was never the same. It was tempting to give this team two more buckets vs. Illinois.
1976 - OSU lost to an IU team that generated a perfect season and an NC by just 2 at home. 2 buckets and we put a nice Buckeye-stamped blemish on their perfect resume.
1980 - 4-seed OSU lost to 8-seed UCLA who would make the NCG, by just 4 in the Sweet 16. A second option that year comes up as we met IU in Assembly Hall with the outright Big Ten title on the line and lost in OT.
1993 - We lost by only 2 to the Fab Five at home a year after Jackson was off to the NCAA. A win not only deals those a-holes a loss, but back to back wins vs 1) Indiana and 5) Michigan allowing us to finish 10-10 is arguably enough to punch our ticket to the dance.
1994 - We lost at home to the Fab Five by 2. A win doesn't do enough for our resume, but if you can't tell by now, I despised those guys and would have loved to see our team hand them a loss.