Answer:
There have been 20 perfect games in the MLB, including Dallas Braden's (OAK) and Roy Halladay's (PHI) perfect games in May 2010. This was the first time in major league baseball that two perfect games were pitched in a single season.
There have been 266 no-hitters since 1875. There have also been 9 combined no hitters, where multiple pitchers keep a no-hitter. Nolan Ryan holds the record for most career no-hitters at 7.