Great question. I think the obvious ones are Duke championship 99, Duke F4 04, and St. Joe's 14.
The S16-E8-F4 games in '11 were all awesome, and that does conflict with Duke F4 above.
Illinois E8 this year is also pretty obvious, although Arizona E8 11 was a nail biter, Gonzaga 99 was iconic for ending their run, Gonzaga 23 was a fun beatdown, and Florida 14 was a statement upset in MSG. Just tough to top the jubilation of 30-0 in Boston, but a competitive category.
SDSU 11 for sweet 16 was great, Kembas flop is iconic, although some of that is hindsight with Kawhi. Was still a fun comeback win. I think poster ahead of me is right though that The Shot has to be it (I was only thinking title years at first) and also how do you top the 06 Anderson/Hamilton buzzer beaters in a comeback? Sweet 16 is definitely the hardest.
I liked Northwestern from 24 for round of 32 because it was such a beatdown. Nova in 14 was a pretty big upset though, so maybe that does have to edge it.
So I think my list is
St Joe's 14
Nova 14
Clemson 90
Illinois 24
Duke 04
Duke 99