From 1946 through 2002 there have been 57 Division I-A Football “National Championships.” According to the NCAA Record Book (pages 79-81), 74 teams from 30 schools have won or shared in the 57 championships (13 times there have been co-champions, twice there have been three teams named).
Thirteen schools have won or shared the title more than once:
Oklahoma (6 outright, 1 tie)
Notre Dame (5 outright, 3 ties)
Miami (4 outright, 1 tie)
Alabama (2 outright, 5 ties)
USC (3 outright, 2 ties)
Nebraska (3 outright, 2 ties)
Ohio State (2 outright, 4 ties)
Texas (2 outright, 1 tie)
Penn State, Florida State, Tennessee (2 outright each)
Michigan State (1 outright, 2 ties)
Michigan (1 outright, 1 tie)
These 13 schools account for 57 out of 74 championship teams (77%). Eight of them are among the BCS top 12 today.
I would argue that to win a national championship you have to schedule (and beat) at least one of the 13.
Seven schools have won the championship once. They are Maryland (1953), Syracuse (1959), Pittsburgh (1976), Georgia (1980), Clemson (1981), BYU (1984) and Florida (1996).
Ten schools have been co-champion once, but have never won the title outright. They are UCLA (1954), Auburn (1957), LSU (1958), Iowa (1958), Minnesota (1960), Mississippi (1960), Arkansas (1964), Colorado (1990), Georgia Tech (1990) and Washington (1991).