Nugent was born in Centerville, Ohio. He attended Centerville High School, and played kicker and quarterback on the football team. He was a teammate of fellow Bengals linebacker A.J. Hawk on the school's football team. As a senior kicker, he converted on five out of seven field goal attempts of greater than fifty yards (24 of 27 altogether), kicked a 55-yard field goal twice, and was 29 out of 29 extra point attempts.
While attending Ohio State University, Nugent played for coach Jim Tressel's Ohio State Buckeyes football team from 2001 to 2004. During his four-year career at Ohio State, he broke or tied 22 school records, including most points in a career by any player at Ohio State (356). He completed 72 of 88 field goal attempts and 140 of 143 extra point attempts. He was recognized as a consensus first-team All-American as a sophomore in 2002 and again as a unanimous All-American senior in 2004, and received the Lou Groza Award as the nation's top college placekicker in 2004. He also was part of the 2002 Ohio State Buckeyes Division I National Championship team. He became the first kicker in Buckeyes team history to earn team most valuable player honors.
Nugent was drafted by the New York Jets in the second round and played four seasons with the team.
During the opening game of the 2008 NFL season, Nugent injured his quadriceps following an extra point. To replace Nugent the Jets signed Jay Feely, who performed so well in the position that he became the Jets' starter while Nugent, who eventually recovered from his injury, was forced to stay on the bench.
An unrestricted free agent in the 2009 offseason, Nugent signed a one-year contract with the Tampa Bay Buccaneers on March 4 and won the job over Matt Bryant in the preseason due to Bryant's injury. After converting just two of his first six tries (2 blocked) through four games, Nugent was released by the Buccaneers on October 5.
Nugent kicking off during the Bengals' training camp in 2012
Nugent signed with the Cincinnati Bengals on April 23, 2010. He competed with Dave Rayner throughout training camp and the preseason for the Bengals starting job. Nugent eventually won the competition when the Bengals released Rayner on September 4, 2010, after Nugent made 54- and 52-yard field goals in the team's final two preseason games. Nugent was named the AFC Special Teams Player of the Month for the month of September by going 8 for 8 on field goal tries in the Bengals' first three games of the season. In 2011, Nugent set franchise records for points (132) and field goals (33). He signed a one-year contract tender with the Bengals for the 2012 season, and on March 10, 2013, the Bengals re-signed Nugent to a two-year deal. On September 7, 2014 Nugent tied the NFL record for most field goals made in one half with 5. On Sunday, January 4th, 2015, Nugent kicked a career long 58 yard field goal during the AFC first round playoff game against the Indianapolis Colts. On October 11, 2015, Nugent made a long winning field goal against the Seattle Seahawks in overtime on Week 5, 2015.