It is not a requirement, so nope. That's not to mean that they haven't over the years.
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Click on the 'NCAA Division 1-A Teams' link on this page to see the 119 teams that make up the Division 1-A in NCAA football.
In Division I football, according to the 2008 NCAA Division I football records manual, the record is 40 and held by Nebraska (1962-2001) and Notre Dame (1889-1932, Notre Dame did not field teams in 1890 and 1891). Click on the 'NCAA Division I Football Records' link below to see the manual. You will need Adobe Reader to be able to view it.
Right now there are 119 division 1 football teams ACC has 12 teams~ SEC-12~ Big 10-11~ Big 12-12~ Pac 10-10~ Big East-8~ Mountian West-9~ Conference USA-12~ WAC-9~ Independent-3~ MAC-13~ Sun Belt-8 but will be 9 when western Kentucky comes in from the other division
Click on the 'Division 1-A Teams' and 'Division 1-AA Teams' links on this page to see all time win loss records as of the start of the 2007 season.
In NCAA division 2 there is a playoff that culminates in a championship game. Imagine that.