I had Spore working for a few days, and then it crashed as I exited. It hasn't worked since.
I've set it to run as administrator, created a shortcut on the desktop, set the compatibility mode for xp sp2, uninstalled and installed it again.... nothing.
When I first installed it, strangely it didn't create a desktop shortcut, no a start menu program group. I had to make a desktop shortcut to get it to work. This is on a single core, Vista 32 bit machine with service pack 1 installed.
I was able to install it and get it working on the 2nd computer (Windows XP).