John Carney, the oldest active player in the NFL (as of the 2010 season) had an inauspicious start to his professional football career. He went undrafted in 1987, was signed by the Cinncinati Bengals that same year, and was subsequently cut before the regular season. As a free agent, he played sparingly for the Tampa Bay Buccaneers between 1988 and 1989, and he also played in 1 game for the Los Angeles Rams in 1989. However, from 1990 to 2000, Carney played for the San Diego Chargers. He was named to the 1994 Pro Bowl, he was named a 1994 All-Pro Player and he is currently the Chargers' all-time leading scorer. Carney went on to kick for various teams (Jaguars, Chiefs, Giants and Saints) up until the 2010 season, when he was released by the Saints. His playing status for the 2011 season is not yet known.
Sidenote - in 2008, forty year olds John Carney and punter Jeff Feagles played for the New York Giants. HELLOOO!