Answer:
According to Baseball Reference, through August 30, 2008 there have been 386,916 MLB games played (this number includes games played in the National Association, the first major league which was in existence from 1871-1875). There have been 257 no hitters of nine innings or more thrown in MLB history. This averages out to one no hitter every 1505.5 games.
Interestingly, on 32 occasions, two or more no hitters have been thrown within 10 days of each other. And on two occasions (April 22, 1898 and June 29, 1990) two no hitters were thrown on the same day.
Not being a statistical major, I can't really tell you the odds of pitching a no hitter. But, looking at the list of ho hitters pitched, the odds are about 1 in 8 that a second no hitter will be pitched within 10 days of a no hitter.
Click on the 'MLB No Hitters' link below to see a list of all no hitters thrown in MLB history.