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.
Rafael Palmeiro with 2831 games without a World Series appearance.
The "World Series" has been played by Major League Baseball since 1903. The World Series is the last round of playoffs, played between the American League champions, and the National League champions.
The National League with the Brooklyn Dodgers for entire career, 10 seasons, from 1947 to 1956.
Yankees
Red Sox and Yankees are in the same league (American) and so they can not meet in the World Series since the World Series is played between the winners of the American League and National League of the Major Baseball League
Major League Baseball has a season that begins in the Spring, runs through the Summer and ends in the Fall. The last games of the season are the World Series games. They normally end by mid October.
The Yankees played in 43 American League Championship Series and won 40 pennants.
At the home ballparks of the National League and American League champions.
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Richie Hebner has: Played Himself - Pittsburgh Pirates Third Baseman in "1970 National League Championship Series" in 1970. Played Himself - Pittsburgh Pirates Third Baseman in "1971 World Series" in 1971. Played Himself - Pittsburgh Pirates Third Baseman in "1971 National League Championship Series" in 1971. Played Himself - Pittsburgh Pirates Third Baseman in "1972 National League Championship Series" in 1972. Played Himself - Pittsburgh Pirates Third Baseman in "1974 National League Championship Series" in 1974. Played Himself - Pittsburgh Pirates Third Baseman in "1975 National League Championship Series" in 1975. Played Himself - Philadelphia Phillies First Baseman in "1977 National League Championship Series" in 1977. Played Himself - Philadelphia Phillies Pinch Hitter in "1977 National League Championship Series" in 1977. Played Himself - Philadelphia Phillies First Baseman in "1978 National League Championship Series" in 1978. Played Himself - Philadelphia Phillies Pinch Hitter in "1978 National League Championship Series" in 1978. Played Himself - Chicago Cubs Pinch Hitter in "1984 National League Championship Series" in 1984. Played himself in "ESPN SportsCentury" in 1999.
South Williamsport where the Little League World Series is held.
The World Series was not played in 1904 (because the National League team refused to play the American League team) and in 1994 (because of a players' strike).