During his United career he kept a total of 48 clean sheets.

He is sometimes called 'The Hero of Munich' because he pulled some of his teammates from the burning plane during the Munich air disaster – including Bobby Charlton, Jackie Blanchflower and Dennis Viollet. Among others he helped were Vera Lukić, the pregnant wife of a Yugoslav diplomat and her two-year-old daughter, Vesna, as well as his badly injured manager Sir Matt Busby. George Best, who used to clean his boots, said, "Bravery is one thing but what Harry did was about more than bravery. It was about goodness."

Gregg is rated by many as one of the best goalkeepers Manchester United ever had. He was unable to win a medal – made all the more frustrating for him by the fact that he played for the club during one of their most successful periods. He was ruled out of the 1963 FA Cup Final victory due to a serious shoulder injury, and a succession of injuries meant that he could not play enough games to qualify for a league championship medal in the 1964–65 season, and he was sold during the first half of their title winning campaign in 1966-67 title winning season. He was also on the losing side in the 1958 FA Cup Final and United's decline in league form that season after losing so many players in the Munich tragedy meant that they finished ninth in a league that they had previously looked capable of winning. A year later United's league form recovered but they finished runners-up to Wolverhampton Wanderers.

He was transferred to Stoke City in December 1966. He played twice for Stoke with mixed success, in his first match he conceded four against Leicester City as Stoke lost 4–2 and then kept a clean sheet in a 2–0 victory over Blackpool before retiring at the end of the 1966–67 season.

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He won 25 caps for the Northern Ireland national team. He was voted best goalkeeper of the tournament at the 1958 World Cup, where Northern Ireland reached the quarter-finals.

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In 1968, he was appointed as manager of Shrewsbury Town. In November 1972, he became manager of Swansea City, resigning in February 1975 to join Crewe Alexandra where he remained until 1978. He then had a spell as goalkeeper coach with his old team Manchester United at the invitation of Dave Sexton, where he stayed until Sexton left in 1981.

His next club was Swindon Town as assistant manager to Lou Macari. Although Macari went on to lead Swindon to the Fourth Division title in 1986, it was without Gregg – he had an open disagreement with Macari which led to them both being sacked in April 1985. During the 1986–87 season he had an uneventful spell as manager of Carlisle United, failing to prevent them from suffering a second successive relegation that pushed them into the Fourth Division for the first time since the 1960s.

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Gregg married his first wife, Mavis Markham, at St James's Church, Doncaster, in 1957, while still a Doncaster Rovers player. Their first child, Linda, was born later that year. A second daughter, Karen, was born a year later. Mavis died of cancer in 1961. On 2 July 1965 Gregg married Carolyn Maunders at St Mary's Parish Church, Rostherne. They have four children; Julie, Jane, Suzanne and John-Henry. He suffered a further tragedy on 24 April 2009 when his daughter Karen died of cancer at the age of 50.

He once owned a hotel (fittingly called the Windsor Hotel) in the town of Portstewart on the North Londonderry coast of his native Northern Ireland. He was appointed a Member of the Order of the British Empire (MBE) in 1995. On 1 July 2008 Gregg was made an Honorary Graduate of the University of Ulster and awarded a Doctor of the University (DUniv) in recognition of his contribution to football at their Summer Graduation Ceremony.

Harry Gregg celebrated his time at Old Trafford on 15 May 2012 with a testimonial organised by John White and John Dempsey from the George Best Carryduff Manchester United SC. The testimonial featured Manchester United playing an Irish League Select XI managed by Martin O'Neill and David Jeffrey. The match ended 4–1 to Manchester United. Gregg, now in his eighties, lives in Coleraine, Northern Ireland. The death of Bill Foulkes in November 2013 leaves Gregg and Sir Bobby Charlton as the only remaining players who survived the Munich crash.

His nephew is football manager and retired player Steve Lomas, who played for clubs including Manchester City and West Ham United, and whose most recent role in football was a brief spell as manager of Millwall.

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Gregg has appeared in a number of recent television programmes about Manchester United and the Munich Air Disaster, including Munich: End of a Dream – a documentary televised in 1998 to mark the 40th anniversary of the Munich tragedy. He was voted best goalkeeper of the tournament in the 1958 FIFA World Cup according to the FIFA documentary "FIFA fever". On the 50th anniversary of the air crash he appeared in the documentary One Life: Munich Air Disaster, broadcast 6 February 2008 on the BBC, in which he returned to the scene of the crash and the hospital for the first time and also met the son of Mrs Lukić, with whom she was pregnant at the time of the disaster. He expressed disappointment at never having been able to meet Mr Lukić, who had died in 2007. He was portrayed by actor Ben Peel in a 2011 BBC film, United, which was centred around the Munich air disaster.

Gregg made an emotional account of the disaster on a TV programme entitled Munich Air Disaster: I Was There on the National Geographic Channel. In particular it centres around a personal journey for a reunion with Vera Lukić, a Serbian woman (the wife of a Yugoslav diplomat), whom Gregg saved from the wreckage, as well as Vera's daughter Vesna, at the time a baby. Unknown to Gregg, Vera was also pregnant at the time of the disaster, so Gregg also rescued another life, that of Vera's son Zoran Lukić whom Gregg was shown meeting in the documentary One Life: Munich Air Disaster.

On 16 April 2012, the National Geographic Channel broadcast an episode of Mayday entitled "Munich Air Disaster", in which Gregg describes the lead up to the disaster and the aftermath.

In April 2015, the feature-length documentary Spirit of '58 was screened as part of the Belfast Film Festival. It featured Harry Gregg prominently alongside the other surviving players of the Northern Ireland national team (Billy Bingham, Peter McParland, Jimmy McIlroy and Billy Simpson) as it told the story of Northern Ireland's journey throughout the 1950s under the managership of Peter Doherty, culminating in the 1958 World Cup in which Gregg was such a success