First things first - there are many vendors other than ASUS (who produce the EEE PC range) who produce comparable machines - I don't have any commercial or personal reason for advocating ASUS devices.
Last weekend I a friend of mine visited most of the electrical stores in and around Reading to figure out which subnotebook best suited their needs - I tagged along as I'm considering buying one for my Sister's Christmas present.
We both did considerable online research and spoke to our friends and trusted advisors to get a feel for which devices to shortlist. We ended up looking at every subnotebook we could lay our hands on while being armed with their technical details to save time in the stores. We both concluded that the EEE PC range were appealing as they had an integrated 1.3Mb webcam, were relatively easy to gain access to for a memory upgrade (if required at a later date) and had good screens.
Picking which machine was quite a complex affair as even having cut down the scope to an ASUS EEE PC there were so many models to choose from.
I can't vouch for the accuracy of the information (though the items I checked were accurate) but I found the Wikipedia EEE PC article very useful indeed - particularly the section a page or two down titled "Specifications".
I think subnotebooks like the EEE PC make sense if your priorities are for a small light weight machine that's inexpensive and has an excellent battery life - if you aren't so interested in getting such a small machine then I think you'd be better off buying a low end full sized laptop as it is likely to be significantly more powerful in terms of CPU and it's ability to run modern operating systems such as Windows Vista - you'll also benefit from a larger screen and keyboard too.
Subnotebooks are fashionable at the moment and I think they have their place though unless you spend considerably more than the typical machines then they are no where near as powerful as "a proper laptop". If you have the money and the inclination you can buy a machine that is powerful AND light weight though you are likely to be looking at well over a thousand English pounds per machine - some of the really fancy ones are over two thousand pounds!
Advent netbook 4211 Intel Atom N270Processor - battery ok 2.5 hours not the best.
Operating Systems - Windows(R) XP Home
Memory & storage - 1GB Memory & 80 GB HDD
10.2" Widescreen Display & 1.2KG - Portable
Extras - Bluetooth connectivity & webcam, been playing with one of these, not bad least its Windows aprox £280 Dixons
Avoid the EEEPCs with the tiny screen. It's useless and painful having to scroll a webpage in both directions. My sister-in-law brought her's when she visited. She got it free when she opened a new bank account with RBC so it was the lowest spec. I used it on and off for a week and I wouldn't buy that particular one. It was underpowered, the screen was too small and the underside got too hot. The only other one I've seen is HP's - but it's more expensive so I don't know what market they're after. The HP's keyboard was crap too, which makes a huge difference. Though I didn't mind Asus' keyboard.
Oh yes, this EEEPC was running Linux. I'm a big fan of Linux (no, really?!) but desktop Linux leaves me quite cold, especially when it comes to browsing content heavy sites that use Flash etc. I had to drop to a console just to install Shockwave (I think), which is an absolute no-no in my books. Content heavy sites ran like crap on the EEEPC and opening more than one tab brought the machine to its knees.
I like the concept of something this size, but I've seen nothing to make me want one yet.
My 2p worth...
I started with a 2nd user Eee 701, which was real fun but limited by the screen size (800x480). This led to a lot of scrolling in web pages and more than a few unusable dialog boxes. So I've recently upgraded to an Eee 901 which is very nice, if a little pricey.
My main requirements are techy/geek so the Eee fits the bill nicely; multiboot options galore, good community support for Linux and will run Windows should I need it for work stuff. The keyboard is a bit crap, but the much better battery life than the competition more than makes up for it. The basic Linux build is pretty decent, and there's promising signs of a fully supported Ubuntu distro (I would like to have full disk encryption :). If I can get it dual booting XP and Ubuntu I'll be a very happy techie :)
I also got hold of an Elonex Onet+, which has a beautiful screen and nicer keyboard than the Eee, but fairly average battery life and somehwat hobbled software distro. Fingers crossed they sort out the software a bit better (the Firefox based browser has some issues, like barfing on the EBay search results page).
It depends very much on your needs; the Acer and HP models have nicer keyboards but suffer from shorter battery life, which may be an issue (although I think you can get a bigger battery for the Acer at least).
If you're after an Eee 701 they're heavily discounted at the moment; if you can live with the smaller screen then they're a steal for ~ £160.
I played around with a friend's EEE PC. I thought the keyboard was unusably small and the mouse trackpad was also too small to use comfortably. It's cheap and it's secure but I didn't get one. In the end, I bought an HP 2133 Mini-Note. It was about £400 so not nearly as cheap but it runs Vista (get a memory upgrade to 2GB or else Vista runs like a dog) and does all the usual PC stuff. Unlike the earlier commenter, I find the keyboard very usable (92% full size) and the screen is great. It's not my main laptop but when I need something small and light it's ideal. Just my two pennies.