Which Major League Baseball team was the first to win consecutive World Series?
The Chicago Cubs won back-to-back World Series in 1907 and 1908.
How many players from the 1995 Major League Baseball World Series are still playing in Major League Baseball?
The most consecutive World Series lost by a team in non-consecutive years is 7 by the Brooklyn Robins/Dodgers (1916, 1920, 1941, 1947, 1949, 1952, 1953) and Chicago Cubs (1910, 1918, 1929, 1932, 1935, 1938, 1945). The most consecutive World Series lost by a team in consecutive years is 3 by the Detroit Tigers (1907, 1908, 1909) and the New York Giants (1911, 1912, 1913).
You did not mention at what level of baseball you are asking. But in every level there is a playoff system. Most levels from Little League to the Major League it is called the World Series. In the Major Leagues the World Series is determined by a best-of-seven game series between one American League team and one National League team. Whoever wins 4 games first wins the World Series.