Just what I could round up from the internet:
AFC East:
Buffalo Bills - Terrance (and Kim) Pegula: Natural gas, oil, and other investments.
Miami Dolphins - Stephen Ross: Tax attorney turned real estate developer.
New England Patriots - Robert Kraft: Founded International Forest Products. Currently owns various businesses held under "The Kraft Group". Does not own Kraft Foods (Kraft Heinz).
NY Jets - Woody and Christopher Johnson, great-grandsons of Johnson & Johnson co-founder, Robert Johnson.
AFC North:
Cincinnati Bengals - Mike Brown, son of team founder, Paul Brown.
Cleveland Browns - Jimmy Haslam, CEO of Pilot Flying J and son of Pilot Corporation founder, Jim Haslam.
Baltimore Ravens - Steve Bisciotti, founder of Aerotek and cofounder of Allegis Group.
Pittsburgh Steelers - Art Rooney II, grandson of team founder, Art Rooney.
AFC South:
Houston Texans - Bob McNair: Founded energy company Cogen Technologies, chairs a real estate firm, and owns an investment company.
Indianapolis Colts - Jim Irsay: Son of Robert Irsay, who interestingly bought the LA Rams then traded for the Baltimore Colts in the same day.
Jacksonville Jaguars - Sahid Khan: Founded Bumper Works, then bought Flex-N-Gate.
Tennessee Titans - KSA (Bud Adams) founded team in the AFL as the Houston Oilers. Made money in oil.
NFC East:
Dallas Cowboys - Jerry Jones: Founded Jones Oil and Land Lease.
NY Giants - John Mara: Grandson of team founder, Tim Mara; Steve Tisch film producer.
Philadelphia Eagles - Jeffrey (and Christina) Lurie: Film producer and (former?) executive at Harcourt General. Grandfather founded General Cinema, which his uncle turned into a massive conglomerate.
Washington Redskins - Dan Snyder: Entrepreneur. Made his first million selling spring break trips to Florida after dropping out of college.
NFC North:
Chicago Bears - Virginia McCaskey: Daughter of team founder, George Halas.
Detroit Lions - Martha Ford: Daughter of Harvey Firestone Jr., chairman of the board at Firestone Tire. Married Henry Ford's grandson, William, who became sole owner of the team in 1963.
Minnesota Vikings - Zygi Wilf: Former attorney turned real estate developer. Turned family business into a large real estate company.
Green Bay Packer - Green Bay Packers, Inc.: Collection of over 360k stockholders. Mark Murphy is chairman.
NFC South:
Atlanta Falcons - Author Blank: Co-founder of The Home Depot.
Carolina Panthers - David Tepper: Founded Appaloosa Management.
New Orleans Saints - Gayle Benson (formerly Tom Benson). Tom Benson started out working in a car dealership, eventually coming to own several of his own. Made most of his money investing in banks.
Tampa Bay Buccaneers - Glazer Family. Heirs of Malcom Glazer, who purchased the team in 1995.
So, it's a mix of self-made businessmen, family ownership, heirs to large corporations, and Packers fans.
Edit: Forgot to the the AFC and NFC West, but I think the picture is pretty clear.