He is most widely known for his NFL record 63 yard field goal, kicked in the final 5 seconds to give the New Orleans Saints a 19-17 win over the Detroit Lions on 8 November 1970. This record still stands (as of the start of the 2003 season), although it was equalled by Jason Elam of the Denver Broncos on 25 October 1998.
Dempsey was born with no right hand, and no toes on his right foot (which was his kicking foot). He wore a modified shoe with a larger toe area.