Record: The Sun Devils have achieved several impressive records throughout their history. Their best record by winning percentage is 12-0 in 1975, while their highest win total is 13 in 1971 and 1972.
Conference championships: Arizona State has won 17 conference championships across different conferences, including the Border Conference, Western Athletic Conference, and Pac-12 Conference. Their most recent championship came in 2013 in the Pac-12 South.
Bowl appearances and wins: The Sun Devils have appeared in 24 bowl games, winning 15. Their most recent bowl win came in the 2021 Las Vegas Bowl.
National rankings: Arizona State has been ranked in the final AP Top 25 poll on 14 occasions. Their highest ranking was No. 2 in both 1975 and 1996.

Here are some arguments for different seasons as the Sun Devils' best:

1975:

Undefeated record of 12-0
Won the Western Athletic Conference championship
Ranked No. 2 in the final AP Poll
Defeated Nebraska in the Fiesta Bowl
1996:

Record of 11-1
Won the Pac-10 Conference championship
Ranked No. 2 in the final AP Poll
Lost to Ohio State in the Rose Bowl

For more on the 1996 season check out the linked article