Who was the player who played in the most World Series games?

Yogi Berra with 14.

Your answer is not correct (check out Walker Cooper with the Cardinals) he had 16 appearances in the World Series.

Walker Cooper appeared in sixteen GAMES of the World Series during the three times his team was in the WS.

Yogi Berra was in 75 GAMES with Yankees during the fourteen times that team was in the WS: 1947, 1949, 1950, 1951, 1952, 1953, 1955, 1956, 1957, 1958, 1960, 1961, 1962, and 1963.