Over the past few months I have installed a number of different Linux distributions on my EeePC 900 and these are my top 5 (in no particular order)....
Mandriva 2009.1 - Mandriva specify that EeePC and netbook hardware support (WLAN, LAN, Audio) is supported from the base install. I've tested Mandriva and it worked very well and the hardware in my EeePC 900 was supported straight off.
OpenSuse 11.1 - A nice distro that has a good set of features and has EeePC hardware support if you add the right repositories and install the required components. Not as easy as Mandriva, but there is a good amount of support information for EeePC specifically maintained on their site.
Fedora 10 - An interesting distribution that I'm running at the moment. WLAN, LAN and Audio worked from base install. The only Linux distribution I've run that has managed to integrate the 4GB and 16Gb SSDs into one single volume. A little more resource hungry than most distributions and so suffers from longer boot times.
EeeBuntu NBR 2.0 - A good distribution specifically for EeePCs. Uses a custom interface designed specifically to suit netbooks and is based on Ubuntu. If you aren't worried about haveing a 'classic' style desktop then this is well worth checking out, and a classic desktop version is also available.
EasyPeasy - Designed specifically for the EeePC and has a full set of driver for the hardware as part of the base installation. Based on Ubuntu and using the same custom netbook interface as EeeBuntu NBR.
If there is another distribution that has good support for EeePC or Netbook platforms then please post it here ...