Although I love Ubuntu, I had to try Mandriva on my EeePC.  The new Mandriva 2008.1 fully supports the EeePC out of the box.  Previously I had eeeXubuntu installed on it.  While it worked, it did not work as nice as I would have liked.

Mandriva, however, is phenomenal on this little laptop.  It looks slick and polished.  

I feel that Mandriva is the best OS for the EeePC at this time. To install it, I used these instructions and did a network install.  It worked perfectly.