Alabama
Notre Dame - 13 Alabama - 12
1965 (Alabama) and 1966 (Notre Dame) they spilt the national championship and in 1962 they won it outright.
Alabama played notre dame in 1957 in the national championship match which alabama won 42 to 26
The 2013 BCS National Championship Game was a contest between the Alabama Crimson Tide and the Notre Dame Fighting Irish.
They have won 11 national football championships
Notre Dame won its first College Football National Championship in 1924.
Notre Dame
1988
The Alabama Crimson Tide defeated the Notre Dame Fighting Irish, 42-14 on January 7, 2013. Alabama, with a final record of 13-1, was also awarded the a "national championship" by the Associated Press, the National Football Foundation and the Football Writers Association of America along with a host of other "minor" championship selectors. Notre Dame, with a final record of 12-1, was awarded a "national championship" by the Colley Matrix, a "minor" championship selector.
Yes, 11 times.