Answer:
Brett Favre has participated in 2 Super Bowl competitions, but has only won one.
The win
Super Bowl XXXI (January 26, 1997, in the Louisiana Superdome in New Orleans, Louisiana):
The Green Bay Packers defeated the New England Patriots 35-21.
The loss
Super Bowl XXXII (January 25, 1998, in the Qualcomm Stadium in San Diego):
The Packers lost to the Denver Broncos, 31-24.