There are two ways to determine the all-time leader in championships.
The first is counting all "national championship" awards from major selectors (meaning the AP, Coaches Poll, UP, BCS, FWAA, et cetera). Using that method, Princeton claims 28 national championships while Yale claims 27 (Michigan is third with 22 and Notre Dame is fourth with 21).
The second recognized method is based upon the "poll era" (1936 to the present). The NCAA recognizes these claims. Alabama leads with nine, Notre Dame has eight, Oklahoma and USC each have seven.
[Results for Alabama and Notre Dame are listed prior to the 2013 BCS National Championship Game]
alabama
Alabama
SEC
Alabama
oklahoma
104
Many teams have won 0 national championships.
The Miami Hurricanes have 5 national championships in football the last being in 2001.
Urban Meyer for one.
SEC
big ten
None.