He played college football for the Ball State Cardinals, twice earning consensus All-American honors.

Maynard was selected by the New York Giants in the third round of the 1997 NFL draft, and was also a member of the Chicago Bears, the Houston Texans and the Cleveland Browns.

Maynard set an NFL record for most punts in a single Super Bowl as the Giants lost 34–7.

His most notable trick play came in 2001, when he threw a 27-yard touchdown pass to Brian Urlacher on a fake field goal en route to a 20–15 victory over the Washington Redskins, which secured the Bears the NFC's second playoff seed.

[10] Along with Patrick Mannelly, kicker Robbie Gould claims Maynard to be one of the Bears' unsung heroes.

On September 13, 2011, the Cleveland Browns signed Maynard to a one-year contract to replace the injured Richmond McGee.