As of Super Bowl XLII, no quarterback nor team has won three consecutive Super Bowls.
Bills 4
Terry Bradshaw
Buffalo Bills (4).
Marv Levy
Miami Dolphins - Super Bowls VI, VII, and VIII.
0-1.
Steve young
Ben Rothleisburger
The most consecutive starts was by Jim Kelly of the Buffalo Bills who started 4 in a row (SBs XXV through XXVIII).
The Buffalo Bills, who lost their appearances in Super Bowls XXV, XXVI, XXVII and XXVIII.
Gale Gilbert was a backup quarterback for the Buffalo Bills for the four years they went to the Super Bowl and lost (Super Bowls XXV-XXVIII) and was the backup quarterback for the San Diego Chargers in Super Bowl XXIX.