The Packers lost once, in 1998.
Two. They lost to the San Francisco 49ers in Super Bowls XVI and XXIII.
The Bills lost four consecutive Super Bowls from 1990-93.
2 (won 1986, lost 2007).
The Chicago Bears have appeared in 2 Super Bowls. The first was in 1986, which they won and the second was in 2007, which they lost.
The Dallas Cowboys have lost 3 super bowls.
He was a member of the Chicago Bears teams that lost to the Indianapolis Colts in Super Bowl XLI.
As of Super Bowl XLII, two. The Patriots lost Super Bowl XX to the Chicago Bears, 46-10 and lost Super Bowl XXXI to the Green Bay Packers, 31-24.
As many as they possibly can.