Well, I have been on many crashes and survived all of it without having not more than few scratches.
@moz's answer mentions about jumping at the car, when it is about to hit you. Haven't tried the side jump yet though. But it is true, it has saved my life many times, usually I end up at the back of the car, due to the car's speed, but I dodge the fatality quite clear.
But you will not always except a low height vehicle like cars, what about trucks, or buses, coming at you with a speed of 70 Kph?
Well, for big trucks with large wheels, is considerable easier to try to go underneath the truck itself, rather than trying to escape from it. Did this once, I fell down on purpose on my bike, by front handle bars and rims were toast, but I lived.
One of the biggest things, that has helped me escape these crashes is I Don't FREAK Out. If you freak out, you are as good as dead. But, as the adrenaline, rushes through your body, and time virtually slows down ("BRAIN reacts faster actually"), you think of yourself and chances to protect it. Dont think about meshing up a expensive bike, and avoiding injury. If you can't take few bruises on your will, surving a crash is highly unlikely.
Crashing on turns, is really scary. But the best move here, as you see crash coming on, jump out of your bike from the back and fall towards the side of the road.
Sometimes, sharp turns can also avoid big crashes. Once, A bike was heading towards me in an unimaginable speed. I really didn't have much time to think. So, I followed basic instincts are tried to take a sharp turn(I just leaned my body towards left side, the best I could). The bike slammed on me, but due the angle I was in, the force ejected me from the bike and pushed me to the sideways, even my bike, wasn't that bad.
However, My scariest crashes are not these. The busy roads. If you luckily survived a crash and are still breathing, there will another crash waiting for you immediately. So, whenever you are down on the road, the best chance you have is, rolling to a safe side (Dont get up, and freak out the driver, they can create a larger accident instead). Watch the approaching vehicle and roll sideways to safetly, continue dodging the vehicles, till you reach the side ways. (I haven't tried this one though, saw it somewhere, I freaked the driver and created a bigger mess).
I have a lot of things to tell, but first lets see, how much was my answer helpful.
BUT STILL THE MANTRA IS
DONT FREAK OUT