It's probably different for different sports, but I have my baseball database open right now so I'll tell you what it is for baseball.
From the start of the 2007 MLB season until August 20th of the 2009 season, there have been 6,702 recorded (not rained out, suspended, etc) MLB games.
Of those 6,702 games, 3,696 games have been won by the favored team, meaning that the favored team won 55.15% of the games.
This number may seem small, but keep in mind that it includes small favorites in the range of -111, not just big favorites like a -320 favorite.
Hope this helps.