- Jun 1 Australian Susie Maroney becomes first person to swim from Mexico to Cuba across shark and jellyfish-infested waters of the Yucatan Straits; swims 123-miles in 38 hours 33 minutes in a cage
- 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 NHL Eastern Conference Final: Washington Capitals beat Buffalo Sabres, 4 games to 2
- Jun 4 Terry Nichols is sentenced to life in prison for his role in the Oklahoma City bombing
Film Release
Jun 5 "The Truman Show", starring Jim Carrey, Laura Linney, and Ed Harris, is released
- 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)
- Jun 5 NHL Western Conference Final: Detroit Red Wings beat Dallas Stars, 4 games to 2
- Jun 6 130th Belmont: Gary Stevens aboard Victory Gallop wins in 2:29
French Open Women's Tennis
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
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
- 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
- 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
Historic Event
Jun 9 Abdulsalami Abubakar succeeds Sani Abacha as military President of Nigeria
NBA Finals
Jun 14 NBA Finals: Chicago Bulls beat Utah Jazz, 87-86 in Game 6 for their 3rd consecutive title and 6th in 8 seasons; MVP: Michael Jordan for 3rd straight year and 6th time
- Jun 14 WLAF World Bowl 6, Waldstadion, Frankfurt: Rhein Fire beats Frankfurt Galaxy, 34-10
Music City News Awards
Jun 15 32nd Music City News Country Awards: Neal McCoy, Lorrie Morgan & Billy Ray Cyrus win
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
Historic Event
Jun 25 New building for The British Library at Kings Cross, designed by Colin St John Wilson, is opened by Queen Elizabeth II in London
Glastonbury Festival
Jun 26 Glastonbury Festival in Pilton, England opens: Primal Scream, Blur, and Pulp headline; other performers include Bob Dylan, Tony Bennett, Nick Cave & The Bad Seeds, Tori Amos, The Foo Fighters, and Hothouse Flowers
