My Asus Eee PC came with Windows XP Home. I've used it as my travel laptop. I got a cigarette lighter adapter and keep the Eee PC in the car.
When I got the Eee PC in the fall of 2008 there was lots of chatter on the forums of installing Vista on it. There were some bootleg drivers out there but no formal support from Asus.
After I got the TechNet Standard subscription, the Eee PC was high on my list for Windows 7. As it turns out, Asus not only supports Windows 7 on the Eee PC with drivers but actually provides a self-upgrade guide to install Windows 7.
It all worked great. I had already installed 2GB of RAM so that wasn't a problem. There are a few subtleties of the Eee PC that don't work. For example, the XP load has the ability to configure the display to 1024x768 and either make it scroll or compress. The vanilla Windows 7 video drivers don't support that. I never used that capability but there are some hacks out there if you must.
Even the Eee PC "bells and whistles" work. For example, the multi-touch track pad (actually from ELAN) is fully functioning along with Asus' Eee Super Hybrid Engine.
Flashing the BIOS was the toughest part. I haven't figured out how to get rid of the grey POST screen but I haven't tried very hard.