I was too young for some of these, but I know about them. Others I saw in person or on TV.
* 1956 -- #7 Iowa defeats #6 Ohio State 6-0 to break the longest winning streak in Big Ten history (OSU had won 17 straight)
* 1957 and 1959 Rose Bowls over Oregon State and Cal
* 1981 -- Iowa upsets #6 Nebraska 10-7 to open the season, and delirious Iowa fans chant "Rose Bowl! Rose Bowl! Rose Bowl" as the final seconds tick away . . . and, as it turns out, they were prophets.
* 1981 -- Iowa upsets #7 UCLA 20-7, and the greatest Hawkeye season in 20 years is rolling.
* 1981 -- Iowa crushes MSU 36-7 while Ohio State is upsetting Michigan to send Iowa to the Rose Bowl for the first time since 1959. Because it came after 20 years of losing seasons, it may be the biggest Iowa win I've ever seen--or ever will see.
* 1982 Peach Bowl -- Iowa beats Tennessee 28-22 in the Peach Bowl in Atlanta, on Dec. 31, Iowa's second bowl game in one calendar year (1982 Rose Bowl on Jan. 1 was the other.)
* 1984 -- Iowa destroys Texas, which had been ranked #1 at midseason, 55-17 in the Freedom Bowl in a driving rain in Anaheim
* 1985 -- #1 Iowa defeats #2 Michigan
* 2005 -- Iowa beats defending national champion LSU and Nick Saban on Tate to Holloway final play
* 2009 -- "7 got 6" on the final play to beat MSU and keep Iowa undefeated (9-0). This also may have been the most physical football game I've ever seen.
* 2017 -- Iowa 55, Ohio State 24, in one of the most dominating performances in Iowa football history.
There are many, many others, but I'll let the rest of you fill in the ones I've left out.