The first date will be that of the 2nd team to win it, and the second date will be that of either team giving up their title. It's been done 20 times... well, maybe 25. If either the Milwaukee Brewers (joining with the reigning NFL Champion Green Bay Packers) or the Texas Rangers (joining with the reigning NBA Champion Dallas Mavericks) win the World Series, they will make it 21 (or 26):
Cleveland, sort of, December 1920 to October 1921: The Cleveland Indians won the 1920 World Series, and the Akron Pros won the first Championship of the American Professional Football Association, which became the NFL in 1922.
New York, December 1927 to December 1928: The New York Yankees won the 1927 and 1928 World Series, the New York Giants won the 1927 NFL Championship, and the New York Rangers won the 1928 Stanley Cup. Which means the Yankees and Rangers were champions at the same time from April 1928 to April 1929.
Boston, sort of, April to October 1929: The Rhode Island-based Providence Steam Roller (for some reason, it was never the plural "Rollers") won the 1928 NFL Championship, and the Boston Bruins won the 1929 Stanley Cup. As many times as the Bruins and Celtics have reached their sport's finals, they have never both won in the same year, although they have won in back-to-back years (Celtics in '69, Bruins in '70).
New York, April 1933 to April 1934: The Rangers won the 1933 Stanley Cup, and the baseball version of the New York Giants won the 1933 World Series.
Chicago, April to December 1934: The Chicago Bears won the 1933 NFL Championship, the first official NFL Championship Game (previous titles were awarded to teams with the best record at the end of the season), and the Chicago Blackhawks won the 1934 Stanley Cup.
Detroit, December 1935 to October 1936: The Detroit Tigers won the 1935 World Series, the Detroit Lions won the 1935 NFL Championship, and the Detroit Red Wings won the 1936 Stanley Cup.
New York, December 1938 to December 1939: The Yankees won the 1938 and 1939 World Series, and the Giants won the 1938 NFL Championship.
New York, April to October 1940: The Yankees won the 1939 World Series, and the Rangers won the 1940 Stanley Cup. The Giants could not defend their NFL Championship, losing the Championship Game in 1939, or else this would have been another threesome.
Detroit, December 1952 to April 1953: The Red Wings won the 1952 Stanley Cup, and the
Lions won the 1952 and 1953 NFL Championship.
Detroit, April to December 1954: The Lions won the 1952 and 1953 NFL Championship, though lost the Championship Game in 1954; and the Red Wings won the 1954 and 1955 Stanley Cups.
New York, December 1956 to October 1957: The Yankees won the 1956 World Series, and the Giants won the 1956 NFL Championship.
New York, October 1969 to January 1970: The New York Jets won Super Bowl III in 1969, and the New York Mets won the 1969 World Series.
New York, May to October 1970: The Mets won the 1969 World Series, and the New York Knicks won the 1970 NBA Title. However, by the time the Knicks won, the Jets had already been dethroned for 4 months, so while this was 3 titles in a short span for New York, it was not 3 titles at once.
Baltimore, January to October 1971: The Baltimore Orioles won the 1970 World Series, and the Baltimore Colts won Super Bowl V in 1971.
San Francisco, specifically Oakland, May to October 1975: The Oakland Athletics won the 1974 World Series (and 1972 and 1973), and the Golden State Warriors won the 1975 NBA Title. The Oakland Raiders couldn't quite make it 3 at once, but they did win Super Bowl XI in 1977.
Pittsburgh, October 1979 to October 1980: The Pittsburgh Steelers won Super Bowl XIII in 1979 and Super Bowl XIV in 1980, and the Pittsburgh Pirates won the 1979 World Series.
Los Angeles, June to October 1982: The Los Angeles Dodgers won the 1981 World Series, and the Los Angeles Lakers won the 1982 NBA Title.
New York, January to October 1987: The Mets won the 1986 World Series, and the Giants won Super Bowl XXI in 1987.
Los Angeles, October 1988 to June 1989: The Lakers won the 1987 and 1988 NBA Titles, and the Dodgers won the 1988 World SEries.
San Francisco, sort of, October 1989 to October 1990: The San Francisco 49ers won Super Bowl XXIII in 1989 and Super Bowl XXIV in 1990, and the Oakland Athletics won the 1989 World Series, against the San Francisco Giants.
New York, sort of, June 2000 to June 2001: The Yankees won the 1999 and 2000 World Series, and the New Jersey Devils won the 2000 Stanley Cup.
Los Angeles, sort of, October 2002 to June 2003: The Lakers won the 2000, 2001 and 2002 NBA Titles, and the team then known as the Anaheim Angels won the 2002 World Series.
Boston, October 2004 to October 2005: The New England Patriots won Super Bowl XXXVIII in 2004 and Super Bowl XXXIX in 2005, and the Boston Red Sox won the 2004 World Series. We now have reason to believe all of these titles are tainted.
Boston, June to October 2008: The Red Sox won the 2007 World Series (tainted), and the Boston Celtics won the 2008 NBA Title (without cheating... as far as we know). In spite of the Celtics' 17 Titles, this is the only time they and another New England team won in the same 12-month period.
Pittsburgh, June 2009 to February 2010: The Steelers won Super Bowl XLIII in 2009, and the Pittsburgh Penguins won the 2009 Stanley Cup.
New York (5 times), Baltimore, Boston, Detroit, New York, and, sort of, Cleveland and San Francisco are the only metro areas to hold the MLB and NFL titles at the same time. If you count the Grey Cup, the championship of the Canadian Football League, then Toronto, with the Argonauts winning in November 1991 and the Blue Jays winning in October 1992, held 2 titles for a matter of days in the fall of 1992.
Los Angeles (twice, and, sort of, a 3rd time), New York, Boston and San Francisco (through Oakland) are the only metro areas to hold the MLB and NBA titles at the same time.
New York is the only city to hold the MLB and NHL titles at the same time.
No city has ever held the NFL and NBA titles at the same time.
Detroit (3 times), New York, Chicago, Pittsburgh, and, sort of, Boston are the only metro areas to hold the NFL and NHL titles at the same time. If you count the Grey Cup, then Toronto has done it 6 times, from December 1914 to March 1915, from March to December 1922, from December 1942 to April 1943, from December 1945 to April 1946, from April 1947 to November 1948, and from April to November 1951; Montreal 4 times, from December 1931 to April 1932, November 1944 to April 1945, May to November 1971, and November 1977 to November 1978; Edmonton once from November 1987 to November 1988; and Ottawa once from April to December 1927.
New York, from the Rangers' Cup in April 1928 to the Giants surrendering the NFL Championship in December; and Detroit, from the Wings' Cup in April 1936 to the Tigers' surrendering the American League Pennant in October; are the only cities to hold 3 titles at once. No city has held 3 titles since the debut of the NBA in 1946.
No city has ever held all 4 titles at once. Only 7 metro areas have won all 4 titles at all: New York (achieving it with the 1970 Knicks), Philadelphia (1974 Flyers), Detroit (1989 Pistons), Chicago (1991 Bulls), Boston (2001-02 Patriots) and, sort of, Los Angeles (2007 Anaheim Ducks). Pittsburgh has won an ABA Title (1968 Pipers), but hasn't had an NBA team since the league's first season, 1946-47. Miami, St. Louis and Washington have won all but the Stanley Cup. Toronto has won 13 Stanley Cups, 2 World Series, and 18 Grey Cups, but never an NBA Title.