Actually, the team in United States professional sports history with the most consecutive games without a loss is the 1979-80 Philadelphia Flyers (NHL), who played 35 consecutive games without a loss (this stretch includes 10 ties).
New England Patriots
The Boston Red Sox have sold out the most consecutive games in MLB history while the Portland Trailblazers have sold out the most consecutive home games in the NBA (and in North America for any sport).
Tom Seaver pitched 10 games that he won in a row in 1969
Glenn Hall 502 consecutive games.
Lou Gehrig played the most consecutive games as a Yankee with 2,130.
UCLA has won the most consecutive NCAA Division I Men's basketball championships, but Kenyon Univ has the most consecutive championships in any sport with 30 in DIII Swimming and Diving. Hobart College has the most consecutive team championships in any sport with 12 in D III Lacrosse.
Cal Ripken Jr. played in 2,632 consecutive games.
Ken Jennings won 74 consecutive games before losing in his 75th.
Whitey Ford w/ 21 consecutive starts w/o loss @ homeCC Sabathia w/ 21 consecutive starts w/o loss @ home