Florida Gators
If you mean in terms of championships won, the answer would be the Nebraska Cornhuskers with three (1994, 1995, 1997) as well as the Florida Gators with three (1996, 2006, 2008). LSU has two (2003, 2007), Alabama has two (1992, 2009), Florida State has two (1993, 1999), Miami has two (1991, 2001), and USC claims two (2003*, 2004).
*AP poll champion. LSU hoisted the BCS Championship Trophy from the BCS Championship Game, in which USC (12-1) did not play, therefore the 2003 championship for USC was controversial, especially after and undefeated Auburn team did not receive any mainstream title recognition.
update 11/29/2008 with UF victory today over FSU
Florida Gators (187-51-1)
Florida State Seminoles (186-51-1)
Florida
Alabama
nebraska
nebraska
Nebraska
Bob Stoops
Alabama
Lsu
Oklahoma
Ohio state
Penn state
I have to assume that you are talking about NFL professional players. Since most of them come from college football teams, most have a college education.
DUKE
Michigan Wolverines
USC
The University of Michigan - Ann Arbor since 1990
Ohio State