So what are the longest titles droughts now? 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 (the NFL's Washington Redskins join in 2 months):
* MLB Minnesota Twins: 25 years, 1 month, 1991-present.
* NHL Edmonton Oilers: 26 years, 5 months, 1990-present.
* NBA Houston Rockets: 26 years, 8 months, 1967-1994.
* MLB Oakland Athletics: 27 years, 1 month, 1989-present.
* MLB Cincinnati Reds: 27 years, 6 months, 1882-1919.
* NHL Calgary Flames: 27 years, 6 months, 1989-present.
* MLB Cleveland Indians: 28 years even, 1920-1948.
* MLB Philadelphia Phillies: 28 years even, 1980-2008.
* MLB Los Angeles Dodgers: 28 years, 1 month, 1988-present.
* NFL Green Bay Packers: 29 years even, 1968-1997.
30 to 40 years:
* MLB Kansas City Royals: 30 years, 1 month, 1985-2015.
* NFL New York Giants: 30 years, 1 month, 1956-1987.
* NBA Dallas Mavericks: 30 years, 6 months, 1980-2011.
* NFL Chicago Bears: 30 years, 10 months, 1986-current.
* NHL Minnesota North Stars/Dallas Stars: 31 years, 6 months, 1967-1999.
* NBA Detroit Pistons: 31 years, 8 months, 1957-1989.
* NBA San Antonio Spurs: 31 years, 8 months, 1967-1999.
* MLB Detroit Tigers: 32 years, 1 month, 1984-current.
* NFL New England Patriots: 32 years, 5 months, 1960-2002.
* NBA Philadelphia 76ers: 32 years, 5 months, 1983-current.
* NFL Oakland Raiders: 32 years, 10 months, 1984-current.
* MLB Baltimore Orioles: 33 years, 1 month, 1983-current.
* NHL New York Islanders: 33 years, 6 months, 1983-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.
* NFL San Francisco 49ers: 35 years, 4 months, 1946-1982.
* MLB Pittsburgh Pirates: 37 years, 1 month, 1979-current.
* NFL Denver Broncos: 37 years, 5 months, 1960-1998.
* NFL Seattle Seahawks: 37 years, 5 months, 1976-2014.
* NBA Seattle SuperSonics/Oklahoma City Thunder: 37 years, 5 months, 1979-current.
* MLB Milwaukee/Atlanta Braves: 38 years even, 1957-1995.
* NBA Washington Bullets/Wizards: 38 years, 5 months, 1978-current.
* NHL Boston Bruins: 39 years, 1 month, 1972-2011.
* NBA Portland Trail Blazers: 39 years, 5 months, 1977-current.
* MLB Seattle Mariners: 39 years, 7 months, 1977-current.
40 to 50 years:
* MLB St. Louis Cardinals: 40 years even, 1886-1926.
* NBA Golden State Warriors: 40 years, 1 month, 1975-2016.
* NBA New York/New Jersey/Brooklyn Nets: 40 years, 5 months, 1976-current. Since their ABA title.
* NHL Philadelphia Flyers: 40 years, 6 months, 1975-current.
* MLB Philadelphia/Kansas City/Oakland Athletics, 42 years even, 1930-1972.
* NBA New Orleans/Utah Jazz: 42 years, 1 month, 1974-current.
* NHL Washington Capitals: 42 years, 1 month, 1974-current.
* NHL Detroit Red Wings: 42 years, 2 months, 1955-1997.
* NFL Pittsburgh Steelers: 42 years, 5 months, 1933-1975.
* NFL Miami Dolphins: 42 years, 10 months, 1973-current.
* MLB Boston/Milwaukee Braves: 43 years even, 1914-1957.
* NFL New Orleans Saints: 43 years, 5 months, 1967-2010.
* NBA Indiana Pacers: 43 years, 6 months, 1973-current. Since their ABA title.
* NBA New York Knicks: 43 years, 6 months, 1973-current.
* MLB Texas Rangers: 44 years, 7 months, 1972-current.
* NHL Los Angeles Kings: 44 years, 8 months, 1967-2012.
* NBA Milwaukee Bucks: 45 years, 6 months, 1971-current.
* NBA Cleveland Cavaliers: 45 years, 7 months, 1970-2016.
* NBA Buffalo Braves/San Diego/Los Angeles Clippers: 46 years even, 1970-current.
* NHL Vancouver Canucks: 46 years, 1 month, 1970-current.
* NHL Buffalo Sabres: 46 years, 1 month, 1970-current.
* NFL Kansas City Chiefs: 46 years, 10 months, 1970-current.
* MLB Seattle Pilots/Milwaukee Brewers: 47 years, 7 months, 1969-current.
* MLB San Diego Padres: 47 years, 7 months, 1969-current.
* MLB Montreal Expos/Washington Nationals: 47 years, 7 months, 1969-current.
* NFL New York Jets: 47 years, 10 months, 1969-current.
* NFL Los Angeles/St. Louis Rams: 48 years, 1 month, 1951-2000.
* NBA Phoenix Suns: 48 years, 1 month, 1968-current. Longest current NBA-only drought in a single city.
* NFL Cincinnati Bengals: 48 years, 2 months, 1968-current.
* MLB Los Angeles/California/Anaheim/Los Angeles Angels: 48 years, 6 months, 1962-2010.
* NBA Denver Nuggets: 49 years even, 1967-current. Longest current NBA drought in a single city. Began in ABA, never won a title in that, either.
* NHL St. Louis Blues: 49 years, 1 month, 1967-current.
* NHL Chicago Blackhawks: 49 years, 2 months, 1961-2010.
* NHL Toronto Maple Leafs: 49 years, 6 months, 1967-current. Longest current NHL drought, if you don't count the old and new Ottawa Senators together. Also longest current drought of any team without even reaching its sport's finals, same length.
50 to 60 years:
* NFL Atlanta Falcons: 50 years, 2 months, 1966-current.
* NFL Buffalo Bills: 51 years, 10 months, 1965-current. Since their AFL title.
* NFL Cleveland Browns: 51 years, 11 months, 1964-current.
* NFL San Diego Chargers: 53 years, 10 months, 1963-current. Since their AFL title.
* NHL New York Rangers: 54 years, 2 months, 1940-1994.
* MLB Houston Astros: 54 years, 7 months, 1962-current.
* MLB Brooklyn Dodgers: 55 years even, 1900-1955.
* NFL Minnesota Vikings: 55 years, 2 months, 1961-current.
* NFL Philadelphia Eagles: 55 years, 10 months, 1960-current.
* NFL Houston Oilers/Tennessee Titans: 55 years, 11 months, 1961-current. Since their AFL title.
* MLB New York/San Francisco Giants: 56 years even, 1954-2010.
* NBA St. Louis/Atlanta Hawks: 58 years, 7 months, 1958-current.
* NFL Detroit Lions: 58 years, 11 months, 1957-current. Longest current drought of any NFL team in a single city.
60 years or more:
* MLB Washington Senators/Minnesota Twins: 63 years even, 1924-1987.
* NBA Rochester/Cincinnati Royals-Kansas City/Sacramento Kings: 65 years, 7 months, 1951-current. Longest current NBA drought.
* MLB St. Louis Browns/Baltimore Orioles: 65 years, 4 months, 1901-1966.
* MLB Cleveland Indians: 68 years, 1 month, 1948-current. Longest current MLB drought, longest drought of any team in a single city.
* NFL Chicago/St. Louis/Arizona Cardinals: 68 years, 11 months, 1947-present. Longest current drought of any team.
* 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: 108 years, 1 month, 1908-2016.
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, and 2013), 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 87 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.