Everett was born in Daingerfield, Texas. He attended Daingerfield High School, where he started playing football as a sophomore. Although his best position was running back, he played seven positions including quarterback. He was the first, and so far only person to have his number retired at Daingerfield High School.
College career
Everett accepted a scholarship from Baylor University, where he played under College Football Hall of Fame coach Grant Teaff. As a freshman, he began the year at running back and was named the starter at cornerback halfway through the season. He also opened the next season at corner, but was moved to free safety in the second game, where he blossomed making 99 tackles. In his junior year he became one of the best defensive backs in the nation, eventually being named a two-time All-American selection, a two-time Southwest Conference Defensive Player of the year and twice first team All-Conference. As a senior, he registered 86 tackles, 14 passes defensed and 6 interceptions. In 1986, Everett became the first-ever winner of the Jim Thorpe Award as the nation's top defensive back. He was also voted the conference's Athlete of the Year. He ranks among Baylor's top ten in career tackles, interceptions, punt returns and punt return yards. Not only was he adept at coverage and as a tackler, but also was a fine punt returner, leading his team in punt return yards three times. He was a leader during one of the school's most successful eras as the Bears won 30 games and appeared in three bowl games. He ranks among Baylor's top 10 in tackles, interceptions and punt return yards. In 2006, he was elected to the College Football Hall of Fame. He was named to Baylor's All-Decade team of the 1980s and to the Baylor Athletics Hall of Fame. In 2015, he was inducted into the Southwest Conference Hall of Fame.
Everett was selected by the Pittsburgh Steelers in the fourth round of the 1987 NFL Draft, after dropping because he was considered too small to play safety. As a rookie, he quickly established himself as a punishing hitter and was named the starter at free safety in the eighth game of the season, finishing second on the team with 72 tackles. He played in Pittsburgh for 5 seasons, intercepted 16 passes over that time, and was considered a top notch safety. On September 19, 1992, after having missed the first two games due to a contract dispute, he was traded to the Dallas Cowboys in exchange for a fifth round draft choice.
Dallas Cowboys
Everett was one of the most important acquisitions made during the Jimmy Johnson era, along with Charles Haley, and helped to solidify the team's defense. He was named the starter at strong safety. In his first season with the Cowboys he wore number 31 because reserve running back Curvin Richards had the number 27, which was the one he wore for five seasons with the Steelers. When Richards was cut after the final regular season game, he changed his number to 27 for the playoffs. The Cowboys went on to win Super Bowl XXVII with him recording two interceptions and a sack in a 52-17 victory over the Buffalo Bills. In 1993, he was moved to his natural free safety position, so that Darren Woodson could start at strong safety. He posted 97 tackles, 2 interceptions, 3 passes defensed and contributed to the Cowboys winning back-to-back Super Bowls. On April 2, 1994, because of salary cap reasons he was traded to the Tampa Bay Buccaneers in exchange for a fourth round draft choice.
Tampa Bay Buccaneers
In 1994, he started 15 games at free safety. The next year, he was limited to 13 games because of a knee injury, registering 54 tackles and one sack. He was waived on March 20, 1996.
