I'd like to tell you how many National Championships each school has won, but unfortunately the answer isn't really quite clear. If you Google, "How many national championships does Notre Dame have?" you get answers like "The Fighting Irish have 13 National Championships recognized by the NCAA..." to "they have been named National Champion 21 times, but only recognize 11 of them."
Ditto for "How many national championships does Alabama have?"
The only thing you can be 100% certain of is that this is the third time in four years that the Crimson Tide have made it to the BCS Championship Game. They have won the previous two appearances. Notre Dame has never played in the BCS Championship Game and has lost all three BCS Bowl Games they have played in. This will be one of the most-watched college football games in history.