I have just got Ubuntu installed and working on my EeePC. I am posting this now from within a Compiz enabled Gnome desktop via my WiFi connection, so it seems quite compatible. I've only just got this up and running, so I can't really comment on the long term usability of it yet, but before I forget, I will make some notes on what I did to get here.
I installed from an alternative install ISO (one with a text-only installer). This is mainly because I quite like the old school feeling, but also because I find it quicker to get done than a livecd. There isn't any real reason not to use the livecd, and that's probably the easiest. Also, I've just realised you are probably wondering how I installed from an alternative install CD without a CD drive. Well I didn't, I have an external CD/DVD drive that I plugged into the USB port and installed from there. To boot an alternative medium, you need to press ESC whle the initial BIOS splash screen is showing, you'll see a list of USB devices as well as the internal SSD, and the internal card reader (which is also USB).
I installed to my 4GB SDHC card rather than the internal SSD, this was important because I've been fiddling for a couple of days now, and I needed to use it for uni earlier today, but since I had not touched the SSD the original Xandros install is still present and correct. To boot my new install I have to hit escape during the BIOS splash and select the SD card. To achieve this, you have to do two things in your install: First pick the SD card as your install medium, and second you need to install grub to the SD card's boot sector not (hd0) as it suggests. Once you've done that and boot for the first time you have to set grub's parameters to (hd0,0) instead of (hd1,0). To do this press "e" when you see the "Ubuntu Linux-2.6.22-14" (or something similar) boot option. You should see the (hd1,0) option on the first line of the next screen, edit it by pressing "e" again, change the number, press enter and press "b" to boot.
The reason for this is that when you install from the CD, you have booted with the internal SSD as the primary hard disk still, and the SD card secondary. In grub notation this makes the internal disk (hd0) and external (hd1). However to confuse you when you select the SD card by pressing ESC at boot, the disks are swapped, and the external becomes the first disk (hd0). Once you have booted, you'll need to go and edit /boot/grub/menu.list, try using
sudo nano /boot/grub/grub.conf
Make sure you get the right lines, or some odd things are likely to happen when you try and boot Ubuntu again. However, you're still fairly safe as you can't break Xandros doing this as far as I can tell.
Once in Ubuntu, there are probably a couple of bits you'll want to do. The thing that caused me most trouble was the fact that I couldn't drag windows out of the screen (very important when the configuration dialogue is twice as high as the screen!) To fix this I installed the advanced Compiz configuration tool using the command:
sudo apt-get install compizconfig-settings-manager
The other big job is getting WiFi working. There are plenty of good tutorials in how to use ndiswrapper out there, basically you need to copy the contents of the /drivers/wireless/ndis5x folder from the ASUS DVD to your hard disk somewhere. Then install ndiswrapper and ndiswrapper-tools using Synaptic.
The rest of the install should follow what's at EeeUser.com(dead link):
You'll also need to blacklist the atheros wifi modules that don't seem to work with this card anyway. Do this by editing /etc/modprobe.d/blacklist, and adding the lines:
blacklist ath_pci blacklist ath_hal
Open a terminal in the folder you copied the Windows driver to and type:
sudo ndiswrapper -i net5211.inf
you shouldn't get any error messages and
ndiswrapper -l should list one device and the net5211 driver. I think you have to run
sudo depmod -a sudo modprobe ndiswrapper
Other than that all I've done so far is remove the bottom taskbar and desktop switcher to save screen space, I'm going to try and get by just using the compiz functions. I've used Macs in the past so it shouldn't be too hard. I also went into the System -> Preferences -> Appearance dialogue and changed all of the system fonts to something a bit smaller, again increasing the usable screen space.
That's all for now, depending on how Ubuntu holds up over the next couple of weeks I may install it on the internal SSD for good.