Note: I am only including those teams that have gone at least 25 years. I am counting from either their last title, or, if they have never won one, from the first game in franchise history.
New York Tri-State Area teams are in bold. Droughts that have ended are in italics.
25 to 30 years:
MLB Los Angeles Dodgers: 25
years even, 1988-present.
NBA Houston Rockets: 26 years,
8 months, 1967-1994.
MLB Cincinnati Reds: 27 years, 6 months, 1882-1919.
NFL Chicago Bears: 27 years, 9 months, 1986-current.
MLB Cleveland Indians: 28 years even, 1920-1948.
MLB Philadelphia Phillies: 28 years even, 1980-2008.
MLB Kansas City Royals: 28 years even, 1985-current.
NFL Green Bay Packers: 29 years even, 1968-1997.
MLB Detroit Tigers: 29 years even, 1984-current.
NFL Oakland Raiders: 29 years, 9 months, 1984-current.
30 to 40 years:
MLB Baltimore Orioles: 30 years even, 1983-current.
NFL New York Giants: 30 years, 1 month, 1956-1987.
NBA Philadelphia 76ers: 30 years, 4 months, 1983-current.
NHL New York Islanders: 30 years, 5 months, 1983-current.
NBA Dallas Mavericks: 30 years, 6 months, 1980-2011.
NBA Detroit Pistons: 31 years, 8 months, 1957-1989.
NBA San Antonio Spurs: 31 years, 8 months, 1967-1999.
NFL New England Patriots: 32 years, 5 months, 1960-2002.
MLB Pittsburgh Pirates: 34 years even, 1979-current.
NBA Seattle SuperSonics/Oklahoma City Thunder: 34 years, 4 months, 1979-current.
MLB Detroit Tigers: 34 years, 6 months, 1901-1935.
MLB Cincinnati Reds: 35 years even, 1940-1975.
MLB Pittsburgh Pirates: 35 years even, 1925-1960.
NBA Washington Bullets/Wizards: 35 years, 4 months, 1978-current.
NFL San Francisco 49ers: 35 years, 4 months, 1946-1982.
NBA Portland Trail Blazers: 36 years, 4 months, 1977-current.
MLB Seattle Mariners: 36 years, 6 months, 1977-current.
NFL Seattle Seahawks: 37 years, 1 month, 1976-current.
NFL Denver Broncos: 37 years, 5 months, 1960-1998.
MLB Milwaukee/Atlanta Braves: 38 years even, 1957-1995.
NBA Golden State Warriors: 38 years, 5 months, 1975-current.
NHL Philadelphia Flyers: 38 years, 5 months, 1975-current.
NHL Boston Bruins: 39 years, 1 month, 1972-2011.
NBA New Orleans/Utah Jazz: 39 years even, 1974-current.
NHL Washington Capitals: 39 years even, 1974-current.
40 to 50 years:
MLB St. Louis Cardinals: 40 years even, 1886-1926.
NBA New York Knicks: 40 years, 5 months, 1973-current.
NFL Miami Dolphins: 40 years, 9 months, 1973-current.
MLB Texas Rangers: 41 years, 6 months, 1972-current.
MLB Philadelphia/Kansas City/Oakland Athletics, 42 years even, 1930-1972.
NBA Milwaukee Bucks: 42 years even, 1971-current.
NHL Detroit Red Wings: 42 years, 2 months, 1955-1997.
NFL Pittsburgh Steelers: 42 years, 5 months, 1933-1975.
MLB Boston/Milwaukee Braves: 43 years even, 1914-1957.
NBA Buffalo Braves/San Diego/Los Angeles
Clippers: 43 years even, 1970-current.
NBA Cleveland Cavaliers: 43 years even, 1970-current.
NHL Vancouver Canucks: 43 years even, 1970-current.
NHL Buffalo Sabres: 43 years even, 1970-current.
NFL New Orleans Saints: 43 years, 5 months, 1967-2010.
NFL Kansas City Chiefs: 43 years, 9 months, 1970-current.
MLB Milwaukee Brewers: 44 years, 6 months, 1969-current.
MLB San Diego Padres: 44 years, 6 months, 1969-current.
MLB Montreal Expos/Washington Nationals: 44 years, 6 months, 1969-current.
NHL Los Angeles Kings: 44 years, 8 months, 1967-2012.
NFL New York Jets: 44 years, 9 months, 1969-current.
NFL Cincinnati Bengals: 45 years, 1 month, 1968-current.
NBA Phoenix Suns: 45 years even, 1968-current.
NBA Indiana Pacers: 46 years even, 1967-current.
NBA Denver Nuggets: 46 years even, 1967-current.
NBA New York/New Jersey/Brooklyn Nets: 46 years even, 1967-current.
NHL St. Louis Blues: 46 years even, 1967-current.
NHL Toronto Maple Leafs: 46 years, 6 months, 1967-current.
NFL Atlanta Falcons: 47 years, 1 month, 1966-current.
NFL Los Angeles/St. Louis Rams: 48 years, 1 month, 1951-2000.
MLB Los Angeles/California/Anaheim/Los Angeles Angels: 48 years, 6 months, 1962-2010.
NHL Chicago Blackhawks: 49 years, 2 months, 1961-2010.
NFL Cleveland Browns: 49 years, 10 months, 1964-current.
50 to 60 years:
MLB Houston Astros: 51 years, 6 months, 1962-current.
NFL Minnesota Vikings: 52 years, 1 month, 1961-current.
NFL Philadelphia Eagles: 52 years, 10 months, 1960-current.
NFL Buffalo Bills: 53 years, 1 month, 1960-current.
NFL San Diego Chargers: 53 years, 1 month, 1960-current.
NFL Houston Oilers/Tennessee Titans: 53 years, 1 month, 1960-current.
NHL New York Rangers: 54 years, 2 months, 1940-1994.
MLB Brooklyn Dodgers: 55 years even, 1900-1955.
NBA St. Louis/Atlanta Hawks: 55 years even, 1958-current.
NFL Detroit Lions: 55 years, 10 months, 1957-current.
MLB New York/San Francisco Giants: 56 years even, 1954-2010.
60 years or more:
NBA Rochester/Cincinnati Royals-Kansas City/Sacramento Kings: 62 years,
4 months, 1951-current.
MLB Washington Senators/Minnesota Twins: 63 years even, 1924-1987.
MLB Cleveland Indians: 65 years even, 1948-current.
MLB St. Louis Browns/Baltimore Orioles: 65 years, 4 months, 1901-1966.
NFL Chicago/St. Louis/Arizona Cardinals: 65 years, 10 months, 1947-present.
MLB Boston Red Sox: 86 years, 1 month, 1918-2004. *
MLB Chicago White Sox: 88 years even, 1917-2005.
MLB Philadelphia Phillies: 98 years, 6 months, 1883-1980.
MLB Chicago Cubs: 113 years even, 1908-current.
The asterisk next to the Red Sox refers not just to the fact that they cheated to win the World Series in 2004 (and 2007), but to the fact that the 1918 MLB season was shortened on orders from the federal government, due to World War I, and the World Series was held in September instead of the usual October.
If you count the current Ottawa Senators franchise with the old one, it's been 86 years, 6 months -- but then, there was a drought of 58 years, 6 months when they didn't even have a team. You could do the same thing with the Baltimore Orioles: An NL team with that name was World Champions in 1896, and the current AL team with that name won in 1966, 70 years later.
Or, to put it another way:
Last won a World Championship since Barack Obama became President: Boston Red Sox, Miami Heat, Chicago Blackhawks, Baltimore Ravens, San Francisco Giants, Los Angeles Kings, New York Giants, St. Louis Cardinals, Dallas Mavericks, Boston Bruins, Green Bay Packers, Los Angeles Lakers, New Orleans Saints, New York Yankees, Pittsburgh Penguins, Pittsburgh Steelers.
Last won under George W. Bush: Philadelphia Phillies, Boston Celtics, Detroit Red Wings, San Antonio Spurs, Anaheim Ducks, Indianapolis Colts, Carolina Hurricanes, Chicago White Sox, New England Patriots, Detroit Pistons, Tampa Bay Lightning, Florida/Miami Marlins, New Jersey Devils, Tampa Bay Buccaneers, Los Angeles Angels of Anaheim, Arizona Diamondbacks, Colorado Avalanche. Began play under him but have never won: Houston Texans.
Last won under Bill Clinton: St. Louis Rams, Dallas Stars, Denver Broncos, Chicago Bulls, Dallas Cowboys, Atlanta Braves, Houston Rockets, San Francisco 49ers, New York Rangers, Toronto Blue Jays, Montreal Canadiens. Began play under him but have never won: Columbus Blue Jackets, Minnesota Wild, Atlanta Thrashers/new Winnipeg Jets, Tampa Bay Rays, Nashville Predators, Vancouver/Memphis Grizzlies, Toronto Raptors, Carolina Panthers, Jacksonville Jaguars, Florida Panthers.
Last won under George H.W. Bush: Washington Redskins, Minnesota Twins, Cincinnati Reds, Edmonton Oilers, Oakland Athletics, Calgary Flames. Began play under him but have never won: Minnesota Timberwolves, Orlando Magic.
Last won under Ronald Reagan: Los Angeles Dodgers, Chicago Bears, Kansas City Royals,
Detroit Tigers, Oakland Raiders, Baltimore Orioles, Philadelphia 76ers, New York Islanders. Began play under him but have never won: Old Charlotte Hornets/New Orleans Pelicans.
Last won under Jimmy Carter: Pittsburgh Pirates, Seattle SuperSonics/Oklahoma City Thunder, Washington Bullets/Wizards, Portland Trail Blazers. Began play under him but have never won: Seattle Mariners: 36 years, 6 months, 1977-current.
Last won under Gerald Ford: Golden State Warriors, Philadelphia Flyers. Began play under him but have never won: Seattle Seahawks, New Orleans/Utah Jazz, Washington Capitals.
Last won under Richard Nixon: New York Knicks, Miami Dolphins, Milwaukee Bucks. Kansas City Chiefs. Began play under him but have never won: Buffalo Braves/San Diego/Los Angeles Clippers, Cleveland Cavaliers, Vancouver Canucks, Buffalo Sabres, Milwaukee Brewers, San Diego Padres, Montreal Expos/Washington Nationals.
Last won under Lyndon Johnson: New York Jets, Toronto Maple Leafs, Cleveland Browns. Began play under him but have never won: Cincinnati Bengals, Phoenix Suns, Indiana Pacers, Denver Nuggets, New York/New Jersey/Brooklyn Nets, St. Louis Blues, Atlanta Falcons.
Last won under John F. Kennedy: None. Began play under him but have never won: Houston Astros, Minnesota Vikings, Washington Senators/Texas Rangers. Until the 2010 Stanley Cup, the Chicago Blackhawks hadn't won since JFK was President.
Last won under Dwight D. Eisenhower: Philadelphia Eagles, St. Louis/Atlanta Hawks, Detroit Lions. Began play under him but have never won: Buffalo Bills, San Diego Chargers, Houston Oilers/Tennessee Titans. Until the 2010 World Series, the Giants hadn't won since Ike was President.
Last won under Harry Truman: Rochester/Cincinnati Royals-Kansas City/Sacramento Kings, Cleveland Indians, Chicago/St. Louis/Arizona Cardinals.
Until the 1994 Stanley Cup, the Rangers hadn't won since Franklin D. Roosevelt was President.
Until the 2004 and 2005 World Series, respectively, the Boston Red Sox and Chicago White Sox hadn't won since Woodrow Wilson was President.
Last won under Theodore Roosevelt: Chicago Cubs.