Well, ncaafootball.net gives Notre Dame and Michigan St. a share of the national championship that year. Notre Dame was awarded the AP and UPI polls among others, while Michigan St. was awarded the National Football Foundation's top spot. Of course, you know they played each other that year and game ended in a 10-10 tie with Notre Dame killing the clock at the end instead of going for the win.
Neither team went to a bowl that year, Notre Dame did not go to bowls back then, while MSU could not go to the Rose Bowl because they had been the year before. That brings us to the University of Alabama. The Crimson Tide had won the previous two AP national championships in 1964 and 1965 with records of 10-1 and 9-1-1. But in 1966 'BAMA went 11-0 with its closest game against Tennesse in Knoxville, an 11-10 win. Alabama thrashed Nebraska 34-7 in the Sugar Bowl to close out an undefeated, untied, an uncrowned 11-0 season.
You can be the judge of who deserved the title that year. Many 'BAMA fans, myself included, believe the Tide was neglected instead of Notre Dame because the AP voters where tired of Bryant's "quick little boys" winning every year. I believe Coach Bryant said as much himself. Many don't like the debate of "mythical championships," but I love college football history. Lesser programs poke fun of Alabama's claim of 12 National Titles, but 1966 is one year 'BAMA got cheated.