OK, this one literally took me hours to sort out.  The solution is a actually pretty simple and is in a few places on the internet, but I'll repeat it here as well. If you get 'XDE Stopped Working' on VMWare:

1) IMPORTANT STEP!!! Update Visual Studio 2012 to Update 4. Even if your install is a fresh SDK downloaded direct from Microsoft you still need to update it.

2) In VMWare set the following processor option:  "Virtualize Intel VT-x/EPT or AMD-V/RVI"

3) Add this to the file 'Windows 8 x64.vmx' : hypervisor.cpuid.v0 = "FALSE"

It was the first step that got me.  It just didn't occur to me that the latest downloadable Windows 8 Phone SDK would be broken.

Here's the back story if you want more info:

I wanted to run the Windows 8 Phone SDK in a virtual machine on Linux.  The reason for this is that I work cross platform.  I've got a MacBook Pro for Xcode and Eclipse/Android, and I've also got Linux (Ubuntu) PC that I use for Android testing amongst other things, as the Emulator is pretty slow on my Macbook.  The Linux PC was my platform of choice for the Windows VM as I find running WM's on my MacBook Pro grind everything to halt (given I'm already maxing out my 8Gb RAM as I leave all my dev tools/graphics apps running).

Firstly, I tried to get things working with VirtualBox.  It wouldn't work. I won't go into what I tried, but just use VMWare Player instead.

The second issue is the Windows runs the Phone emulator using Hyper-V.  I won't go into the standard way of setting up Hyper-V as it's well documented elsewhere, but when you try to run it on a standard install you'll get a message telling you it won't work because 'Hypervisor is already running'.  In other words it won't let you run one hypervisor on another.  VMWare lets you get round this:

a) shutdown your VMWare
b) Go to the machine settings/processor
c) select the following option 'In VMWare set the following processor option:  "Virtualize Intel VT-x/EPT or AMD-V/RVI"'
d) Find the file called 'Windows 8 x64.vmx', open it with a text editor, and add the following line at the end:  hypervisor.cpuid.v0 = "FALSE" 

Try again.  This time you will find you can start Hyper-V, but when you try to run the emulator it will crash, saying 'XDE Stopped working'.   To fix this:

a) Download and run 'Visual Studio 2012 Update 4'.  It's the same update for Express and the full version.
b) Reboot (it is Windows after all).
c) Try again.  It should start working.