Stapleton was a tough tackling forward who was an especially good header of the ball. He started his career with Arsenal, joining them in 1972 as an apprentice, after being turned down by Manchester United. He made his first-team debut in 1975 against Stoke City, and would go on to form a potent striking partnership with Malcolm Macdonald; the two scored 46 goals between them in 1976–77. He was Arsenal's top scorer for the three following seasons, and helped the Gunners reach a trio of FA Cup finals; Stapleton scored one of the goals in Arsenal's 1979 FA Cup Final 3–2 win over Manchester United, and scored 108 goals in 300 appearances in total for the Gunners.
Stapleton went on to move to Manchester United in 1981 for £900,000 (a fee set by tribunal after the two clubs could not agree). He helped United win the 1983 and 1985 FA Cups. It was in the first of those finals, when he scored against Brighton, in which Stapleton made history by becoming the first man to score for two different clubs in FA Cup Finals. He left United in 1987, after scoring 78 goals for the club in 365 matches.
He went on to play for Ajax Amsterdam, before returning to England with Derby County, Blackburn Rovers, Aldershot, Huddersfield Town (as player-coach) and Bradford City, where he spent three seasons after a brief period at Le Havre in France.
After being sacked as Bradford's player-manager in 1994, he had a brief spell at Brighton & Hove Albion in the 1994–95 season, playing two games before finally announcing his retirement as a player.
He also won 71 caps for the Republic of Ireland, scoring a then record 20 goals. Stapleton made his international debut under then player-manager Johnny Giles in a friendly against Turkey in Ankara in 1976 at 20 years of age. He scored after only three minutes of his debut when he headed home a Giles free-kick at the near post. That friendly international finished 3–3 and marked the start of a magnificent international career for the quiet and reserved Stapleton.
Stapleton was committed to international football insisting that an "international release clause" be inserted to all of his contracts so that he could be released to play in international games for Ireland.
Stapleton played a significant role in Ireland's attempt to qualify for the World Cup in Spain in 1982. Goals against Cyprus, the Netherlands and France for Stapleton in the qualifying matches were not enough as Ireland were denied a place at the World Cup by a superior French goal difference. Stapleton was made captain of the national team for the qualifying campaign for the 1986 World Cup though Ireland failed to emulate their fine performance in the 1982 qualifiers.
Jack Charlton took over as the Irish manager in 1986 and he kept Stapleton as captain despite a sometimes uneasy relationship between the two men. Stapleton scored a magnificent diving header in the opening Euro 1988 qualifier against Belgium in the 2–2 draw at the Heysel Stadium, Brussels that September. He also scored in the 2–1 defeat by Bulgaria in Sofia on 1 April 1987 with another goal against Luxembourg in the 2–1 victory at Lansdowne Road the following September.
Stapleton captained the Irish team to the 1988 Euro finals and played in all of their matches during the competition including Ireland's famous victory against England.
After the 1988 European Championships Stapleton remained on the fringe of the national team during qualification for World Cup Italia 1990 making just two appearances late in the campaign. By then, his 20 goals for the Republic had made him the national side's all-time leading goalscorer – a record which would be broken 10 years later by Niall Quinn, who was in the early stages of his own international career when Stapleton bowed out of the international scene.
He did, however, score an 87th-minute goal against Malta in a 3–0 friendly in Valletta just prior to those finals in Italy.
Stapleton moved to the United States to manage Major League Soccer side New England Revolution in 1996. In the 2003–04 season he briefly returned to English football as a specialist coach of Bolton Wanderers. The Bolton manager Sam Allardyce wanted Stapleton to enhance the skills of the strikers at the club and saw the Irishman as an ideal candidate, given his successful playing career.
Stapleton was appointed assistant manager to former teammate Ray Wilkins with Jordan on 3 September 2014.Arsenal
FA Cup (1): 1979
FA Cup (2): 1983, 1985
FA Charity Shield (1): 1983