19. Oregon lost to Ohio State in the 1958 Rose Bowl, 10-7, but didn't punt once.
Oregon also lost to Ohio State in the 2010 Rose Bowl, but in '58, they were a missed field goal away from tying the Woody Hayes-coached Buckeyes. But Oregon didn't punt the ball once--much like the current Ducks. The thing is that Oregon didn't win its conference that year. Oregon State had beat Oregon that year, but the Beavers couldn't play in the game because they had played in the Rose Bowl the year before, and the Pacific Coast Conference had a no-repeat rule.