As of Super Bowl XLII, that would be Joe Montana of the San Francisco 49ers with 13 consecutive completions in Super Bowl XXIV.
Bills 4
Terry Bradshaw
Buffalo Bills (4).
16 by Tom Brady in Super Bowl 46 in a loss to the New York Giants
Tom Brady in Super Bowl 46. The record stands at 16
Buffalo Bills, 4 in a row.
the Miami dolphins 71&72
Brett Farve
The Buffalo Bills have the most consecutive appearances in a Super Bowl. The went to Super Bowls XXV, XXVI, XXVII, and XXVIII. The lost all four games.
Tom Brady, of the New England Patriots, in Super Bowl XLVI (46). On February 5, 2012.
Tom Brady as of 2-5-12.