The above answer is right but it's also misleading. Your odds of dying in an airplane is about 1 in 11 million (and much, much lower in the United States which has some of the most strict safety laws in the world).
You should be much more worried about the drive to the airport. Your odds of dying on that is about 1 in five thousand.
Bottom line: while some airlines undoubtedly are different, their relative safety ratings probably don't matter. In that article posted in the answer by Eric W, the least safe airline had 30 incidents in a year. When you consider that most incidents don't cause crashes (making that Daily Beast methodology sketchy), if your plane does crash you have a 95.7% chance of surviving and there are very few incidents to begin with, airline safety ratings are really not a big deal. Enjoy the flight!