Michigan won the most games
Rutgers and Princeton played the first ever game of American Football at the college level in the 1869, with Rutgers winning by a score of 6-4. College football has changed quite a bit since then, with the addition of the PAT, the forward pass, and more. Logic would suggest that because of the long history, these two schools have played the most games. Michigan 877 wins. Most all time.
As of the start of the 2007 season, Alabama has played in the most bowl games with 54. They have won 30 of those games. Alabama.
According to College Football Data Warehouse, as of the 2007 season Alabama has played in the most bowl games with 54. Their record is 30-21-3.
Michigan in FBS