I will respectfully disagree with your stating, "better team than the 80 or 87".
The game changed a lot from 69 to 87. Heck, it has changed a lot(especially in Iowa) in the last 22 years).
In 1969, there were probably a handful of teams (at best) that could have been considered a contender.
Now, you can say 10-15 teams. Recruiting has changed it. AAU circuits have changed it.
Iowa's 87 team had (7), count 'em, SEVEN future NBA players on the roster.
Would be a fun game, but I will take the 87 Iowa team against any Iowa team in the 100+ year history.
As for the answer to the original question: duh. 87 UNLV loss. Worst coaching job I have ever seen. No offense to UNLV, they were good.
Football: ISU 2002 is popular. But, I do not see us winning the title that year even if we made it. Look at how USC absolutely demoralized us in the bowl game.