Minnesota were recognized as the AP National Champions, and also won the UPI and AFF National Championships that year (all 3 being recognized by the NCAA as consensus national champions).
Ole Miss won the Football Writers Association of America (FWAA) National Championship, the only other award recognized by the NCAA.
Other "National Champions" included Iowa, Missouri and Washington, but none of their championships are recognized by the NCAA.
Ohio State won the NCAA National Championship in 1960 by a SLAM DUNK!!!
UEFA European Football Championship was created in 1960.
Rex White won the Nascar Grand National Series championship in 1960.
Japanese Roller Hockey National Championship was created in 1960.
The Philadelpphia Eagles which was the last time they won a national championship.
The 1960 Missouri Tigers finished 5 in the final AP Poll; while the UPI poll has them #4.
Ole Miss won the 1960 national championship. Ole Miss finished the 1960 season with a 10-0-1 record and an SEC championship and Sugar Bowl championship. The AP recognized Minnesota as the 1960 national champion, with Ole Miss at number two. However, the AP final poll was released prior to the bowl games. Minnesota was defeated in the Rose Bowl and finished with an 8-2 record. The NCAA and the SEC both recognize Mississippi's 1960 national championship. Various other services list Ole Miss as 1959 and 1962 national champions as well.
Burkina Faso national football team was created in 1960.
The UEFA European Football Championship was first held in 1960.