i just had these problems. With Parallels, you get a kernel panic and the equivalent of the blue screen of death. What happens is you get the message to hit the power button in a nice window floating on top. It's never been a problem with the Macbook Pro or Macbook. There is a hotfix apparently from Parallels just for the MBA:
It keeps crashing. There are already some discussions about this on the Parallels forum. I have just bought the Macbook air and is very frustrated because Parallels keep crashing with increasing frequency with my MBA.
The update of Parallels Desktop for Mac with the hotfix for MacBook Air kernel crashes is now available. This thread is closed by Xenos. Please ask any questions you have on the build 5592 in this thread.
I'm getting a kernel crash using parallels under osx 10.5.1 (and also under 10.5.2). I think it has to do with the x3100 graphics in the air, but am not certain. Anyone else having this problem? My crash log says it is a result of com.parallels.kext.vmmain(3.0).
The update of Parallels Desktop for Mac with the hotfix for MacBook Air kernel crashes is now available.
This is a special build recommended for MacBook Air users only. In all other cases the build 5584 is still relevant.
Please download the build 5592 here.