I'm posting this from my ASUS EeePC 1000HE, which I purchased one month ago. I primarily use it for web browsing, note-taking/research/novel planning (MS OneNote), and writing (MS Word).
My opinion of the 1000HE is: I adore it. What I was looking for was a light, cheap (less than $400) netbook, with great battery life (6 hours or more), a reasonably large screen for its size (10", 1024x600 resolution), and a comfortable, nearly full-sized keyboard that would both feel satisfying to type on, and be tolerable for lengthy writing sessions.
Thus far I have been completely impressed with this little machine. Its battery life is phenomenal (regularly 6-8 hours with multiple programs in use and screen brightness at medium), its screen is adequate and not as crippling as I'd worried it might be, and the "chiclet-style" keyboard (e.g., Macbook keyboard) is wonderful.
I upgraded my unit to 2G of RAM, and I'm running Windows 7 RC1 on it along with Microsoft Office 2007, and can even use Adobe Creative Suite 4 for non-intensive image editing. Where the machine shows its limits is when watching video in a web browser (embedded Flash). YouTube SD is watchable, but anything more intensive than that will choke. This is more of a problem with Flash than with the machine, though, as Flash is notoriously CPU-intensive.
Just beware of this limitation, which applies to all netbooks based on Intel Atom processors, and have realistic expectations in mind: as a web browser, word processor, music player, etc., netbooks are excellent.
I have two quibbles with the 1000HE. First, its keyboard: although the keys are large for a netbook (93% of standard laptop-sized keys) and have good tactile response, these units do have a tendency to randomly repeat keystrokes. There are some keyboard settings you can turn on in various OSes to deal with this, but ultimately nothing seems to solve the problem. It's not annoying enough to be obtrusive for me while writing, but I'm a fast touch-typist and don't mind having to correct occasional typos. Others may find it too irritating to bear, however.
My only real complaint with the 1000HE is its over-sensitive trackpad. While it has some nice iPhone-like finger gestures for scrolling and zooming, the pad is way too sensitive and sometimes registers movement while you're carefully typing, making the cursor leap to somewhere else on the page--and you'll suddenly notice you're typing in the middle of a paragraph. Frustrating. There are some user-created tweaking programs to deal with this, but the solution involves disabling the trackpad completely, which I don't want to do while I'm mobile. This problem typically isn't obtrusive enough to interfere with my writing more than a couple times over an hours-long session, but when it does happen, the results can be disastrous. Just a warning.
Overall, this criticism aside, I'm incredibly pleased with my purchase and am finding that the portability and battery life, along with the satisfying keyboard, are conducive to me taking the netbook with me nearly everywhere and writing on the go--which is more than I could have hoped for. It's also fantastic for carrying around the house and browsing while doing various domestic tasks, or just relaxing on the couch.
I've had several people at work notice my little netbook that's now always by my main workstation, and they've all been impressed with the price, battery life, and size. Netbooks definitely seem to hit a previously unrealized need for an extremely portable machine that can browse/email and do light productivity and media tasks.
Finally, personal anecdote: I bought an iPhone a few months ago, because I needed a portable internet device that I could take with me at all times. While I love the iPhone, I've found it too slow and cumbersome (both hardware-wise and AT&T network-wise) for doing anything but the most cursory web searches. I haven't ended up using it as much as I'd expected, or in as casual a way as I'd expected. The netbook, however, completely dominates my web browsing at home--and I have a powerful quad-core desktop with an enormous 30" LCD. It's just so much more convenient and cozy to use the netbook, rather than sit at my monolithic desktop and Browse the Web (capital letters).
Hope this verbose response contains something of use to you. Bottom line: get to an electronics store and try out as many netbooks as you can before deciding on one. They're such a personal type of device that it behooves you to find one you're truly comfortable with.