Well, the probability of being involved in two plane crashes is less than that of being involved in one. Think about the odds of drawing an ace from two different unsorted decks of cards at the same time, and you'll understand that idea. However, the second time you get on a plane, the odds of you getting in a crash are the same. That's like saying that the odds of pulling an ace from the second deck is the same as pulling an ace from the first, even if you happen to have pulled an ace from the first.
In short, being in a plane crash once does not reduce the probability of being in a second plane crash. But the probability of being in two plane crashes is much lower than being in only one crash, because you must crash twice. To give you a simpler example: if you flip a coin, the probability that you will get heads is 0.5. The second time you flip, the probability is the same. However, the odds of getting heads twice in a row is (0.5)^2. If the probability of crashing in a plane is P, the probability of crashing twice in a row is P^2. If P is small, the odds against getting in two consecutive plane crashes may be very high! I don't know quite how to handle nonconsecutive plane crashes, but I suspect the odds against getting in multiple nonconsecutive plane crashes are high as well.
I see that Unstable has hit the nail on the head. You can only calculate the probability of both events happening before both of them happen. But if one happens first, the overall probability calculation changes. After one crash, you are still just as likely to get in another. However, before any crash happens, the probability of you getting into two crashes is very low.