I recommend it and I don't recommend it.
A friend of mine has an eeePC and it's a neat little gadget. The machine itself is rather small, light, and thin... a very portable PC that you can lounge around with in the house with a wireless network. The specs are nothing to really gawk at, but that's a strength of the eeePC, if you think about it.
I would love to have one, but at the same time, I don't need one because I already have an HP tc1100 tablet PC, which is about the size or slightly larger than the eeePC.
I would recommend it to someone who doesn't want to spend the money for a full-fledged machine that primarily uses the computer for word processing, Internet, e-mail, and instant messaging. Productivity would be the name of the game with this Asus computer... I wouldn't push it to play any of the newer games today, but I hear that people have gotten World of Warcraft to work on it, which could be a joy for some people willing to stick with the classics of yesteryear (or anything that doesn't call for heavy system requirements to run).
My thoughts could change if I ever get one, but I don't see that happening.