There have been two no hitters pitched in the MLB playoffs:
Don Larsen's perfect game in game 5 of the 1956 World Series; And Roy Halladay's No Hitter (28 batters) on October, 6th 2010 in game one of the NLDS.
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According to the announcers of the Atlanta Braves vs. the Colorado Rockies on April 17, 2010 the answer is 264 no hitters in major league history. Colorado Rockie Ubaldo Jiminez completed the most recent MLB no hitter in Atlanta this evening. If one assumes approximately 150,000 games in the history of the MLB that equates to about 0.00176, less than .2% of games result in a no-hitter. If you see on, you are very lucky.
As of September 26, 2007 there have been 255 no-hitters thrown in the history of MLB. Click on the 'MLB No-hitters' link on this page to see a list of them.