A native of the Bronx, Strickland played for the New York Gauchos. While a junior he led Truman High School in Co-Op City to the state championship and was ranked as one of the top 10 high school recruits in the nation. As a senior, he transferred to Oak Hill Academy in Virginia.
Strickland became a college star at DePaul University where he appeared in 87 games. As a junior, he was a First Team All-American after averaging 20.0 points and 7.8 assists. A 1987 and 1988 All-America pick, Strickland helped lead the Blue Demons to four-straight NCAA Tournament appearances from 1985–88, including Sweet Sixteen showings in 1986 and 1987. The four-time Blue Demon letterwinner ranks among the program's career leaders in scoring average (8th; 16.6 ppg), assists (3rd; 557) and steals (2nd; 204). He also averaged 3.4 rebounds while shooting 53.4% during his college career.
He was selected in the first round of the 1988 NBA draft by his hometown New York Knicks where he backed up point guard Mark Jackson, the 1988 NBA Rookie of the Year. He was seen as sort of an odd choice by some observers since the Knicks had Jackson. Nevertheless, Jackson and Strickland shared time that season. Strickland played in all 82 games and averaged 8.9 points and 3.9 assists in 16.8 minutes per game where he was named to the NBA All-Rookie Second Team.
Knowing that having both Jackson and Strickland play for the same position would not work, the Knicks dealt Strickland to the San Antonio Spurs for veteran Maurice Cheeks in the middle of the 1989–1990 season. Strickland flourished in San Antonio. The Spurs went 18-6 with him in the starting lineup. He led the club in assists 26 times and averaged 12.3 points and 11.2 assists in 10 playoff games.
In the 1990–91 season Strickland lived up to his expectations as an exciting performer when he was healthy. He missed 24 games that year because of a sore ankle and a broken bone in his right hand. In the 58 games he played, Strickland averaged 13.8 points and 8.0 assists, shooting .482 from the field and .763 from the free throw line. He led the Spurs in assists 46 times and in steals 30 times. Strickland finished the year tied with Terry Porter for 12th in the NBA in assists. And in a four-game series loss to the Golden State Warriors in the first round of the 1991 NBA Playoffs, he posted terrific numbers: 18.8 points, 5.3 rebounds, 8.8 assists, and 2.25 steals in 42.0 minutes per game.
Starting the 1991–92 NBA season in a contract dispute with the Spurs management, Strickland didn't play in the first 24 games of the season. He finally signed on December 23, then started 54 of 57 games and averaged 13.8 points, 8.6 assists, 4.6 rebounds, and 2.07 steals in 36.0 minutes per game. He scored in double figures 48 times and scored 20 or more points on eight occasions. He notched a then career-high 28 points against the Indiana Pacers on February 6 and made a career-high 19 assists versus the Minnesota Timberwolves on March 3. Strickland started two playoff games against the Phoenix Suns before missing the third with a broken bone in his left hand. The Suns swept the series in three games.
Before the start of the 1992–93 season, Strickland signed as a free agent with the Portland Trail Blazers. In four seasons with the Blazers, Strickland averaged 17 ppg and 8.6 apg.
In a move that initially helped both franchises, Strickland and teammate Harvey Grant were traded to the Washington Bullets for Rasheed Wallace and Mitchell Butler in 1996. In his first season in Washington, Strickland averaged 17.2 ppg and 8.9 apg helping the Bullets make the playoffs in 1997 for the first time in 8 seasons.
In 1997–98, Strickland had the best season of his career as he averaged 17.8 ppg and a league leading 10.5 apg. During the year, Strickland also became only the 25th player in NBA history to record 10,000 points and 5,000 assists. Strickland was selected to the Second Team All-NBA. While his individual stats improved over the next few seasons for the Wizards, the team got worse, leading to a buyout of his contract.
Strickland would go on to spend time with the Miami Heat, Minnesota Timberwolves, Orlando Magic, Toronto Raptors, and the Houston Rockets to conclude his NBA career. He played in 1,094 games (740 starts) and scored over 14,000 points and dished out nearly 8,000 assists. He also ranked among the NBA's top 10 in assists per game in 1991–92 (5th), 1993–94 (6th), 1994–95 (5th), 1995–96 (4th), 1996–97 (5th), 1997–98 (1st), and 1998–99 (2nd).
Strickland averaged 13.2 points, 3.7 rebounds, 7.3 assists, 1.5 steals and 30.7 minutes of floor time per game.
Strickland was hired as an assistant coach at USF under former Kentucky assistant Orlando Antigua. Prior to that, he served in an administrative role at the University of Kentucky under Coach John Calipari. Strickland started his coaching career as director of basketball operations at the University of Memphis, taking over the job held by former NBA player, Milt Wagner. In September 2008, Strickland was inducted into the New York City Basketball Hall of Fame along with NBA stars Kenny Anderson and Sam Perkins, coach Pete Gillen and pioneers Lou Bender and Eddie Younger.
Strickland is the godfather of 2011 NBA Draft first overall pick and 2012 Rookie of the Year Kyrie Irving.