I'll add this. Sean Lahman's Database is also widely used. Though it's mainly whole season statistics, not game by game. Along with post-season, all star games, schools, salaries.

http://www.seanlahman.com/baseball-archive/statistics/

Then of course MLB has a bunch of data here, mainly the PitchF/X data since 2008 is gathered from here.

http://gd2.mlb.com/components/game/mlb/