It depends on what you use for the selector. Major College/D1A/FBS teams have never had an official National Champion. (assuming you mean the before mentioned divisions). See the related link below.
In Football it is Princeton with 28 titles. In Basketball it is UCLA with 11 titles.
116 national championships since 1895 in football. However most teams don't count their national championship pre ww2!
Paul "Bear" Bryant for Alabama.
University of North Carolina at Chapel Hill
According to wikipedia. Princeton has the most titles with 28.
usc has 20 jk
The University of Alabama Crimson Tide
Top Ten College football Programs by stats.1: Michigan - 11 National Titles, Most winning program in college football history, most winning seasons of any college football program, most undefeated seasons of any program, most games played without being shut out, 42 Big Ten Titles, Tied second most conference championship titles than any other program in college football history.2: Notre Dame - 13 Recognized National Titles, Third most winning program in College football History, Seven Heisman winners, most All-Americans of any program.3: USC - 11 Claimed National Titles, Seven Heisman Winners. 38 Pac-10 Titles, Third most conference titles by any other program.4: Ohio State - 7 Claimed National Titles, Seven Heisman winners, fifth most winning program of all time, Second Most All-Americans All-time, Most overall Award winners all-time. 33 Big Ten titles, Fourth Most conference championships than any other program. Fewest losing seasons of any college football program of all time with only eight (minimum 10 seasons). (Played against Michigan to Determine Conference champion numerous times)5: Alabama - 12 Claimed National Titles, more bowl wins and appearances than any program.6: Nebraska - 5 Claimed National Titles, fourth most winning program of all time, 3 Heisman Trophy Winners 46 conference championships, More conference championships than any other program in college football history.7: Oklahoma - 7 Claimed National Titles, Five Heisman Trophy Winners, 42 Conference Titles. Tied second most conference championships all-time.8: Texas - 4 Claimed National titles, second most winning team in college football history, 2 Heisman Trophy winners, 29 Conference Titles.9: Miami - 5 Claimed National Titles, 2 Heisman Winners (Started in 1926 so extra points)10: Penn State - 2 Claimed National Titles, Sixth most winning team of all-time.