- Jun 1 European Central Bank is founded in Brussels to define and execute the European Union's monetary policy
- Jun 2 The CIH computer virus is discovered in Taiwan
- Jun 3 Eschede train disaster: an ICE high speed train derails in Lower Saxony, Germany, causing 101 deaths
- Jun 4 Terry Nichols is sentenced to life in prison for his role in the Oklahoma City bombing
- Jun 4 NHL Eastern Conference Final: Washington Capitals beat Buffalo Sabres, 4 games to 2
- Jun 5 A strike begins at the General Motors parts factory in Flint, Michigan, that quickly spreads to five other assembly plants (the strike lasted seven weeks)
Film Release
Jun 5 "The Truman Show", starring Jim Carrey, Laura Linney, and Ed Harris, is released
Jim Carrey
Ed Harris
Television Premiere
Jun 6 TV sitcom "Sex and the City" premieres in the US on HBO, starring Sarah Jessica Parker, Kim Cattrall, Kristin Davis and Cynthia Nixon
Tennis Open
Jun 6 French Open Women's Tennis: Arantxa Sánchez Vicario of Spain beats Monica Seles 7-6, 0-6, 6-2; her 4th and last career Grand Slam singles title and 3rd French title
Monica Seles
- Jun 7 James Byrd, Jr. is dragged to death by Shawn Allen Berry, Lawrence Russel Brewer, and John William King in Jasper, Texas in a racially-motivated hate crime
- Jun 7 52nd Tony Awards: "The Lion King" and '"Art" win
- Jun 7 French Open Men's Tennis: In an all-Spanish final Carlos Moya beats Alex Corretja 6-3, 7-5, 6-3 for his lone major title
Event of Interest
Jun 9 Abdulsalami Abubakar succeeds Sani Abacha as military President of Nigeria
Sani Abacha
- Jun 11 Compaq Computer pays $9 billion for Digital Equipment Corporation in the largest high-tech acquisition.
- Jun 14 "Comic Relief" benefit comedy show
- Jun 14 52nd NBA Championship: Chicago Bulls beat Utah Jazz, 4 games to 2
- Jun 15 32nd Music City News Country Awards: Neal McCoy, Lorrie Morgan & Billy Ray Cyrus wins
- Jun 16 Stanley Cup Final, MCI Center, Washington D.C.: Detroit Red Wings go back-to-back, defeating debutant finalists Washington Capitals, 4-1 for a 4-0 series sweep
US Golf Open
Jun 21 US Open Men's Golf, Olympic Club, SF: Lee Janzen recovers from 7 stroke deficit to win his second Open title, 1 stroke ahead of runner-up Payne Stewart
Payne Stewart
- Jun 21 "Don't Be Cruel" 2nd studio album by Bobby Brown is released (Grammy Award Best Male R&B Vocal Performance 1990)
- Jun 24 NBA Draft: Pacific center Michael Olowokandi first pick by Los Angeles Clippers
- Jun 25 In Clinton v. City of New York, the United States Supreme Court decides that the Line Item Veto Act of 1996 is unconstitutional
- Jun 27 Opening of the Kuala Lumpur International Airport in Malaysia.
- Jun 27 NHL Draft: Rimouski Oceanic (QMJHL) center Vincent Lecavalier first pick by Tampa Bay Lightning
- Jun 30 Sega Channel, cable's 1st on-demand video game service, closes down