I got this cute eeepc model 701 4G in June 2008, it was one of the first netbooks in my country and quite expensive at that time (350€). But I just couldn't resist getting one with GNU/Linux installed. Before these netbooks appeared it was rather difficult to find a laptop without "that other" hideous legacy operating system pre-installed. You had to pay for it even if you didn't intend to use it at all. (Getting a refund was just myth and legend)
The eeepc came with Xandros but do you want to know how little it lasted there? Just a couple of weeks and Debian took over!!!
I love my eeepc so much that I just can't imagine my life without it. I use it more than any other of my machines. I installed Etch (=lenny testing), Lenny and now Squeeze. If everything goes well I'll install Wheezy, and hopefully whatever comes next.
I use it with a full-blown desktop environment (id est gnome) and I even have openoffice!!! (I removed it at first but changed my mind later) But if I have to tell you the truth I had to get rid of a lot of bloat. (cups, exim...) due to space constraints. At the moment of writing this I use it everyday with these applications: amsn, xchat, radiotray, metv, supertux, dropbox, filezilla and chromium browser. Some of them at the same time and it works tirelessly!!!
Well the story goes that in order to tweak this pretty little thing I used two awesome tools: a debian-live system and the savoir-faire of Debian-eeepc project. In order to learn more about this project I recommend you to take a look at their site. I could talk about this project for hours because I have read and learned a lot on their site. But I'll let you judge by yourself.
Update 1 (March 4th): I tried this image from the debian eeepc wiki. It is awesome in live mode (with lxde) but the installer crashed in the middle of the process. Anyway it is a release candidate 1. The stable release, if any, ought to work just fine.