The Detroit Tigers lost 1907, 1908, and 1909.
The NY Giants lost 1911, 1912, and 1913.
The Yankees lost 1921 and 1922, as well as 1963 and 1964.
The NY Giants lost 1923 and 1924, as well as 1936 and 1937 (all four to the New York Yankees!)
The Brooklyn Dodgers lost 1952 and 1953; and the Los Angeles Dodgers lost 1977 and 1978 (again, all four to the Yankees!).
Atlanta Braves lost 1991 and 1992.
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The teams that have played in the World Series in consecutive years would include the Chicago Cubs due to playing in the 1906, 1907 and 1908 series, the Detroit Tigers were in the 1907, 1908 and 1909 series, the Philadelphia Athletics played in the 1910 and 1911 series, the New York Giants played in the 1911, 1912 and 1913 series, the Boston Red Sox played in the 1915 and 1916 series, the New York Yankees played in the 1921, 1922 and 1923 series, the Washington Senators played in the 1924 and 1925 series, the St. Louis Cardinals played in the 1942, 1943 and 1944 series, the Brooklyn Dodgers played in the 1952 and 1953 series, the Milwaukee Braves played in the 1957 and 1958 series, the Los Angeles Dodgers played in the 1965 and 1966 series, the Baltimore Orioles played in the 1969 and 1970 series, the Oakland Athletics played in the 1972, 1973 and 1974 series, the Cincinnati Reds played in the 1975 and 1976 series, the Atlanta Braves in the 1991 and 1992 series, the Toronto Blue Jays in the 1992 and 1993 series, the Texas Rangers in the 2010 and 2011 series and the Kansas City Royals in the 2014 and 2015 series.
The last team to lose back-to-back World Series was the los Angeles dodgers to the new York yankees in 1977 - 1978