- Jun 3 George Burley, Scottish football player and manager
- Jun 3 Suren Nalbandyan, Soviet Armenian Greco-Roman wrestler (Olympic gold 1976), born in Geghard, Armenia, Soviet Union
- Jun 4 John Treacy, Irish marathoner (Olympic silver 1984), born in Villierstown, County Waterford
- Jun 4 Martin Adams, English darts player (BDO World Champion 2007, 10-11), born in Sutton, Surrey, England
- Jun 4 Terry Kennedy, American baseball player, born in Euclid, Ohio
- Jun 6 Andy Pycroft, cricketer (Zimbabwe Test batsman)
Björn Borg (67 years old)
Jun 6 Swedish tennis player (11-time Grand Slam winner), born in Stockholm, Sweden
- Jun 7 Robert Dover, American equestrian dressage (Olympic bronze 1996), born in Chicago, Illinois
Joe Montana (67 years old)
Jun 11 American Pro Football HOF quarterback (Super Bowl 1981 [MVP], 84 [MVP], 88, 89 [MVP]; NFL MVP 1989, 90; 3×First-team All-Pro; 8xPro Bowl; SF 49ers; KC Chiefs), born in New Eagle, Pennsylvania
- Jun 12 Terry Alderman, Australian cricketer (prolific Australian medium-pacer 1981-91), born in Subiaco, Perth, Australia
Fred Funk (67 years old)
Jun 14 American golfer (The Tradition 2008, 10; US Senior Open 2009), born in Takoma Park, Maryland
- Jun 15 Lance Parrish 'Big Wheel', American baseball catcher (MLB All Star x 8; World Series 1984 Detroit Tigers; 3 × Gold Glove), born in Clairton, Pennsylvania
- Jun 17 Nick Cook, English cricketer (left arm slow bowler in 15 Tests 1983-89), born in Leicester
- Jun 20 Peter Reid, English soccer midfielder (13 caps; Bolton Wanderers, Everton, Manchester City) and manager (Manchester City, Sunderland, England U21, Leeds United), born in Huyton, England
- Jun 21 Mikhail Burtsev, Soviet sabre fencer (Olympic gold 1976, 1980), born in Moscow (d. 2015)
- Jun 21 Rick Sutcliffe, American baseball pitcher (LA Dodgers, Chicago Cubs), born in Independence, Missouri
- Jun 22 Alfons De Wolf, Belgian cyclist
- Jun 23 Tony Hill, American football player
- Jun 27 Brad Childress, American football coach, born in Aurora, Illinois
- Jun 27 Jeff Odintz, American horse trainer, born in Brooklyn, New York
- Jun 29 Pedro Guerrero, Dominican MLB player (LA Dodgers), born in San Pedro de Macorís, Dominican Republic
About June 1956
How Old? 67 years old
Generation: Baby Boomer
Leap Year: Yes