Dallas Cowboys vs. The NFL

Opponent, regular season record (post season)

Arizona/Phoenix/St. Louis Cardinals, 55-27-1 (0-1 in the post season)
Atlanta Falcons, 12-8 (2-0 in the post season)
Baltimore Ravens, 0-2
Buffalo Bills, 4-3 (2-0 in the post season)
Originally compiled by Hostile from a sports forum:

Carolina Panthers, 5-1 (0-2 in the post season)
Chicago Bears, 9-9 (2-0 in the post season)
Cinncinati Bengals, 5-4
Cleveland Browns, 10-15 (1-2 in the post season)
Denver Broncos, 4-5 (1-0 in the post season)
Detroit Lions, 10-7 (1-1 in the post season)
Green Bay Packers, 11-9 (4-2 in the post season)
Houston Texans, 0-1
Indianapolis/Baltimore Colts, 7-5 (0-1 in the post season)
Jacksonville Jaguars, 2-1
Kansas City Chiefs, 5-3
Miami Dolphins, 3-7 (1-0 in the post season)
Minnesota Vikings, 9-10 (4-2 in the post season)
New England Patriots, 7-2
New Orleans Saints, 14-7
New York Giants, 50-37-2
New York Jets, 6-2
Oakland/Los Angeles Raiders, 3-6
Philadelphia Eagles, 51-38 (2-1 in the post season)
Pittsburgh Steelers, 14-12 (1-2 in the post season)
San Diego Chargers, 6-2
San Francisco 49ers, 9-14-1 (5-2 in the post season)
Seattle Seahawks, 6-4
St. Louis/Los Angeles Rams, 9-10 (4-2 in the post season)
Tampa Bay Buccaneers, 6-3 (2-0 in the post season)
Tennessee/Houston Titans/Oilers, 6-5
Washington Redskins, 54-34-2 (0-2 in the post season)