When I first heard about the EeePC, I brushed it off as a gimmick -- that was, until a friend of mine picked one up and had me tinker around with it. I never thought such a small notebook could actually be useful, but boy was I wrong. The keyboard is OK to type on, and the 7" display is adequate for surfing the web/viewing documents/ebooks/etc.
I actually ended up buying one this past weekend, and just love it. To me, it's the perfect mobile companion (I used to have a 17" gaming laptop, but it was just too big for my needs -- I barely ended up taking it places because it was too bulky). Sure, I could probably make due with an ultralight laptop like the Lenovo Thinkpad X300, but those machines are far too pricey for me.
Yes, I realize this won't be nearly as powerful as my desktop is, but I don't need it for that. When I'm on the go, the most processor-intensive thing I would do is watch videos -- and the EeePC has enough horsepower for that.