The Chicago Bulls were World Champions in 96,97 and 98.
The Los Angeles Lakers were World Champions in 00, 01 and 02.
So the answer to your question is the Chicago Bulls and Los Angeles Lakers.
Lyon is the Ligue 1 club that has the most consecutive Ligue 1 titles.
That would be Michael Jordan who won 10 scoring titles during his career. 1986-87 through 1992-93 (seven consecutive seasons) and 1995-96 through 1997-98 (three consecutive seasons).
Bloomsburg, PA has the most state titles with 23 consecutive state titles in a row. led by Matt tombasco
The New York Yankees have the most consecutive World Series titles with 5, from 1949-1953.
The NBA team is Miami Heat.
Women's US Open Tennis Record Holders: 1968-currentWinner of most Singles titles: (6) Chris EvertWinner of most consecutive Singles titles: (4) Chris EvertWinner of most Doubles titles: (9) Martina NavratilovaWinner of most consecutive Doubles titles: (3) Virginia Ruano Pascual, Paola SuarezWinner of most Mixed Doubles titles: (3) Margaret Court, Billie Jean King, Martina NavratilovaWinner of most Championships (total: singles, doubles, mixed): (18) Margaret Court, (16) Martina NavratilovaMen's US Open Tennis Record Holders: 1968-currentWinner of most Singles titles: (5) Jimmy Connors, Pete Sampras, Roger FedererWinner of most consecutive Singles titles: (5) Roger FedererWinner of most Doubles titles: (4) Bob Lutz, Stan Smith, John McEnroeWinner of most consecutive Doubles titles: (2) Todd Woodbridge, Mark WoodfordeWinner of most Mixed Doubles titles: (3) Todd Woodbridge, Bob BryanWinner of most Championships (total: singles, doubles, mixed): (8) John McEnroe
The New York Yankees won 5 consecutive World Series titles from 1949 - 1953.
The driver who won the most consecutive driver's championship is Michael Schumacher. This is with 5 titles from 2000-2004. The team who won the most consecutive constructors championship is Ferrari, This is with 6 championships from 1999-2004,
Manchester United has won thrice the league titles 1998-2001 and 2006-2009
Men: Roger Federer / Bjorn Borg each with 5 straight titles Ladies: Martina Navratalova with 6 straight titles