The cars they blow up are not the cars they drove up in, but normally just a shell (plenty in the junk yard) painted to look good. I watched Myth Busters, and they had a good show on this. (The myth busters love blowing things up, and are former stunt men).
The cars that crash are reinforced with roll bars etc. And are driven by stunt men. Once it has been crashed, you can easily change the body and use it in the next show.