None. They have only made 2 World Series appearances, in 2010 and 2011, and they lost both.
The Yankees made 40 World Series appearances and won 27 times.
The Seattle Mariners have been in the Major Leagues since 1977 (33 years) and have never been in the World Series. If you're asking about the longest drought of a team who HAS been in a World Series before but hasn't been in one since, the Chicago Cubs were last in the World Series in 1945, but haven't been in one since, making that a 65 year stint.
The Texas Rangers made back-to-back World Series appearances in 2010 and 2011. They lost the 2010 World Series in five games to the San Francisco Giants. A year later, they lost the 2011 World Series to the St. Louis Cardinals.
Homestead Grays with 5 appearances and 3 championships. The Kansas City Monarchs played in 4 NLWS and won twice.
2010-2011 were the first ever appearances for the Texas Rangers in a World Series. The team made the playoffs in 1996, 1998, 1999, but were eliminated by the Yankees each time.
In the 1990's, the Yankees made three World Series appearances.1996 (defeated the Atlanta Braves 4-2)1998 (defeated the San Diego Padres 4-0)1999 (defeated the Atlanta Braves 4-0)
As of the start of the 2007 season, the New York Yankees have won 26 World Series championships, more than any other franchise and more than the combined number of titles won by the next three most successful clubs in the World Series. The St. Louis Cardinals have won 10 World Series and the Philadelphia/Oakland Athletics have won 9 World Series Titles. -------------------- The Yankees have been in 39 World Series. The second most World Series appearances is by the Dodgers with 18. The Giants and Cardinals have been in 17.
Florida has not won a college World Series but has made it to 9.