Oakland Raiders (although they played in L.A. from 1982 through 1994)
Minnesota Vikings (they started out in Bloomington and later moved a few miles away to Minneapolis, but they've always been in the same metro area)
Dallas Cowboys (technically, they've played in a couple of Dallas suburbs, but still the same metro area)
New York Jets (they originally played in New York City and now play in northern New Jersey, but it's still considered part of the NYC metro area)
New York Giants (see the Jets)
Philadelphia Eagles (technically, Philadelphia and Pittsburgh swapped franchises in 1940, with players moving to the opposite cities but the team names remaining the same; but most people consider the Eagles and Steelers as continuous franchises from the year they both joined the league)
Pittsburgh Steelers (see the Eagles)
Teams that have moved:
Chicago Bears (originally from Decatur, Illinois)
Detroit Lions (originally from Portsmouth, Ohio)
Washington Redskins (originally from Boston)
Carolina Panthers (played their first season in South Carolina and now play in North Carolina)
St. Louis Rams (originally from Cleveland, and later from Los Angeles)
Arizona Cardinals (originally from Chicago, and later from St. Louis)
New England Patriots (originally from Boston; they now play about halfway between Boston and Providence, Rhode Island)
Baltimore Ravens (technically a continuation of the original Cleveland Browns franchise)