The Cleveland Cavaliers recently won the NBA title for the first time, ending the city of Cleveland's long period of suffering. The last time Cleveland had a title team was way back in 1964, when their Browns won the NFL league championship. So I got to thinking--who's next? I decided to check into this. I stuck with cities who have teams in the "big four" sports--Major League Baseball (MLB), the National Football League (NFL), the National Basketball Association (NBA), and the National Hockey League (NHL). Since Canada has a team, or more, in the NBA, MLB, and especially the NHL, I'm including them, too. And yes, the "big four" only applies to American/Canadian sports in part due to my lazy nationalism, I guess. These are the sports I (and most Americans) care the most about.
Also, as many folks know, teams often have stadiums/arenas outside the limits of the city in their name, or even outside the state in the case of some New York teams, which sometimes compete across the river in New Jersey. I'm including teams with their associated name, and within a metropolitan area. Meaning San Francisco, Oakland, and San Jose are considered one metro area, and the New Jersey Devils (who play in Newark, NJ) are counted as a New York City team, etc.
Finally, many cities have never had a league champion. So this list will start with them, in order of how long they've had at least one team in these four sports. Therefore, a city with teams starting in 1975 will count as a longer drought than one with a team starting in 2000, of course. The parentheses after the city's name refers to how many sports teams the city has, or 1 through 4. NBA and NHL seasons overlap years, so 1979-80 for example, instead of 1979 for a MLB and NFL team. And I won't be discussing cities that had teams but lost them, and never got another one later. Only those currently with a big four team.
1) No League Title Ever. (Tie) San Diego (2) and Buffalo (2), had at least one team since 1960. (They each did win an American Football League (AFL) title in the years before they were absorbed into the NFL, though, with San Diego's coming in 1963, and Buffalo's in 1964 and 1965.)
2) No League Title. Vancouver (1), NHL team since 1970-71.
3) No League Title. Salt Lake City/Utah (1), NBA team since 1979-80.
4) No League Title. Sacremento (1), NBA team since 1985-86.
5) No League Title. Orlando (1) NBA team since 1989-90.
6) No League Title. Ottawa (1), NHL team since 1992-93.
7) No League Title. (Tie) Jacksonville(1), and Charlotte (2), NFL teams since 1995.
8) No League Title. Memphis/Nashville/Tennessee, (2), NFL team since 1997. (I realize Memphis and Nashville aren't in the same metro area, but the NFL team was called "Tennessee" and moved their playing field from Memphis to Nashville, so I'm counting them together.)
9) No League Title. Columbus, OH (1), NHL team since 2000-01
10) No League Title. Oklahoma City (1), NBA team since 2008-09.
11) No League Title. Winnipeg (1). NHL team since 2011. (They had a team starting in 1979-80, but lost it to another city, and were then given another NHL franchise in 2011.)
12) No League Title. Brooklyn (1). NBA team since 2012-13. If you want to count the Nets as separate from the other New York City teams. Their Dodgers did win a MLB title in 1955, before they moved to Los Angeles.
The following cities have won at least one league title in their history. Once again, in order from longest ago to most recent. In the event of cities winning in the same year, I'll list it in order of the title game(s) which are played first, i.e., the NHL usually finishes up before the NBA, then MLB, then the NFL (whose final game is played in the next calendar year, technically).
13) 1970-71. Milwaukee (2), whose NBA Bucks team won.
14) 1976-77. Portland (1), OR, whose NBA Trail Blazers won.
15) 1988-89. Calgary (1), whose NHL Flames won.
16) 1989-90. Edmonton (1), whose NHL Oilers won.
17) 1990. Cincinnati (2), whose MLB Reds won.
18) 1991. Minnesota (4), whose MLB Twins won.
19) 1991. Washington (4), whose NFL Redskins won.
20) 1992-93. Montreal (1), whose NHL Canadians won.
21) 1993. Toronto (3), whose MLB Blue Jays won.
22) 1994-95. Houston (3), whose NBA Rockets won.
23) 1995. Atlanta (3), whose MLB Braves won.
24) 2001. Phoenix/Arizona (4), whose MLB Diamondbacks won.
25) 2003-04. Tampa Bay (3), whose NHL Lightning won.
26) 2006. Indianapolis/Indiana (2), whose NFL Colts won.
27) 2007-08. Detroit (4), whose NBA Pistons won.
28) 2008. Philadelphia (4), whose MLB Phillies won.
29) 2009. New Orleans (2), whose NFL Saints won.
30) 2010. Green Bay (1), whose NFL Packers won.
31) 2010-11. Dallas (4), whose NBA Mavericks won.
32) 2011. St. Louis (2), whose MLB Cardinals won.
33) 2011. New York (4), whose NFL Giants won.
34) 2012. Baltimore (2), whose NFL Ravens won.
35) 2012-13. Miami (4), whose NBA Heat won.
36) 2013. Seattle (2), whose NFL Seahawks won.
37) 2013-14. Los Angeles (4), whose NHL Kings won.
38) 2013-14. San Antonio (1), whose NBA Spurs won.
39) 2014. Boston (4), whose NFL Patriots won.
40) 2014-15. Chicago (4), whose NHL Blackhawks won.
41) 2014-15. San Francisco (4), whose NBA Warriors won.
42) 2015. Kansas City (2), whose MLB Royals won. (Current MLB champs)
43) 2015. Denver (4), whose NFL Broncos won. (Current NFL champs)
44) 2015-16. Pittsburgh (3), whose NHL Penguins won. (Current NHL champs.)
45) 2015-16. Cleveland (3), whose Cavaliers won. (Current NBA champs.)
So, if we're considering one of the 13 cities which have all teams in all four sports, (some, like New York, actually have more than one team in one sport, even) the longest drought is Minneapolis/Minnesota, which last won in 1991, followed closely by Washington, D.C., who won their last title later in the 1991 season (Super Bowl played in early 1992).
But, of course, the longest title futility for a team, not a city, is the poor Chicago Cubs of MLB, who haven't won one since 1908. (Although they're much improved in the past couple of years, so that might change soon.)
(Update: As most even casual fans know, the Chicago Cubs finally broke their long streak, as they won the World Series in late 2016.)