4 (1991, 1992, 1993, and 1994)
The Bills lost four consecutive Super Bowls from 1990-93.
The Bills have appeared in 4 Super Bowls but their record in those Super Bowls is 0-4
The Bills have never won the Superbowl.
The Buffalo Bills have never won a Super Bowl. They appeared in 4 straight Super Bowls from 1990-1993, but did not win any of them.
The Buffalo Bills have won 0 Super Bowls.
One Super Bowl
Zero, they are 0-4 in the Super Bowl.
The Buffalo Bills appeared in and lost 4 consecutive Super Bowls.
The Washington Redskins lost 2 Super Bowls XII and XVIII.