How many times in World Series history has a team won games 3, 4, and 5 at home?

This has happened 14 times through 2012.

1955 Brooklyn Dodgers -- defeated Yankees, 4-3.

1956 New York Yankees -- defeated Dodgers, 4-3.

1965 Los Angeles Dodgers -- defeated Twins, 4-3. (Sorry, David.)

1969 New York Mets -- defeated Orioles, 4-1.

1971 Pittsburgh Pirates -- defeated Orioles, 4-3.

1974 Oakland Athletics -- defeated Dodgers, 4-1.

1978 New York Yankees -- defeated Dodgers, 4-2.

1981 Los Angeles Dodgers -- defeated Yankees, 4-2.

1984 Detroit Tigers -- defeated Padres, 4-1. (At least the Dodgers weren't involved this time.)

1987 St. Louis Cardinals -- lost to Twins, 4-3.

1991 Atlanta Braves -- lost to Twins, 4-3.

2001 New York Yankees -- lost to Diamondbacks, 4-3.

2006 St. Louis Cardinals -- defeated Tigers, 4-1.

2008 Philadelphia Phillies -- defeated Rays, 4-1.

The 2-3-2, best of seven format was not reliably established until 1924 (and has been deviated from since then only during 1943-45, probably due to wartime travel restrictions; yeah, WW2 was over by October 1945, but the guess here is that restrictions continued until the forces were fully mustered out in '46). By 1924, baseball had gotten over its 5-of-9 experiments, and the convenient single-city Series played between the Giants and Yankees, both of whom played at home in Polo Grounds, or within shouting distance across the East River when Da Stadium opened in '23; games simply alternated site or designated home team. So prior to 1924, the question does not accurately apply. Worth noting, though, the 1920 Cleveland Indians won Games 4, 5, 6, and 7 at home to knock off the Brooklyn Robins (Dodgers by a previous name; clearly the franchise simply loooooves this "win the middle games at home" phenomenon), five games to two.