The Chicago Bears, with 700 victories in their history.
The Michigan Wolverines by a little bit. With 11 national championships and the winningest college football team in history who plays in the biggest stadium in the country. They also have a winning record against every conference. Suprisingly they probably do best against the SEC out of all BCS conferences.
If you are asking about college football, I believe all fifty states have at least one college with a football team, and some have many more than one. If you are asking about professional football, there are a number of states that do not have a team at this time: among them are Maine, Mississippi, Alaska, Hawaii, Vermont, and North Dakota.
Ohio state buckeyes GO BUCKS
The Michigan Wolverines are the most winningest college football team in FBS history.
Winningest sec football team of all-time is Alabama.
Boise State 112 wins with a .868 winning percentage