Alabama does!
Many teams have won 0 national championships.
North Carolina, Duke, NC State and Maryland
Yes, Alabama in 1978 and 1979 and Georgia in 1980. But, three different SEC teams have never won three national championships in A Row Also When Florida Beat Ohio State in 2006 LSU Beat Ohio State in 2008 and Florida Beat Oklahoma in 2009
Alabama
Alabama for the 2009 season and Auburn for 2010 season.
The Ohio State University has 7 national championships. When they beat the University of Miami in 2002 that gave them their seventh championship since 1952.
116 national championships since 1895 in football. However most teams don't count their national championship pre ww2!
Texas longhorns
In certain confrences with very good teams, such as the SEC this is not uncommon.
The teams over the years that played for football National Championships in college?
None. Since the expansion to 16 teams.