Pomera DM10 Pocket Word Processor
I've wanted something like the Pomera DM10 for years: a single-purpose instant-on word processor that folds up small and light enough to put in a pocket and (almost) forget it's there.
It's got a 4-inch monochrome 640x480 LCD display, displays 17 lines of text, and stores your work as plain text to whatever you've shoved in its SD card slot. It runs for 20 hours on a single pair of AAA batteries, too. Multi-day battery life and instant-on: want.
The problem, of course, is that it lacks connectivity and they want $300 for what is otherwise an extremely basic item. At that price, one's thoughts move from "no-frills pocket writing tool" to "Kindle with a decent keyboard."

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I have owned two Dell Axim's with foldable keyboards that do this and a lot more all with full colour monitors and 300 - 600 Mhz processors. They worked incredibly well for taking hours and hours of notes in university lectures (and occasionally for taking notes from books while studying). While the setup is excellent for portability and off-the-cuff notes for activities like paper writing that require multi-page editing and mouse-features, I would prefer a full PC-environment.
My current setup is an Axim x50 with a bluetooth keyboard. My x30 which I ordered with a plug in keyboard was the perfect combo.
For the word processor software itself - I've used SoftMaker Office for Pocket Pcs - http://www.softmaker.com/english/ofp_en.htm
For 3 bills, why not just get an Alphasmart Dana? Then you get all the Palm capability too, plus a bigger screen.
Alphasmarts are cool.
I think I'm going to have to hack something out of an old PDA and a BT keyboard if I'm to get what I want.
The Alphasmart Dana -- I owned one -- has problems; the screen contrast is poor, it runs PalmOS 4 (now more than somewhat antiquated), the included WP software is a marginally hacked-on version of a package that hasn't been updated since 2001, and so on. It'd be a great concept if they'd update it, but as things stand it's about five years past it's sell-by.
I'm with IanM: I have an HP iPaq 214 (the UK equivalent of the US iPaq 210) and a Think Outside folding keyboard, and TextMaker (the WP from SoftMaker) when I want to write. If you poke around on eBay you can probably pick up a machine in that class, and the keyboard, for around $350. Cons: the battery life is only about 6 hours. Pros: everything else. (Full-fat word processor, colour VGA screen, all sorts of other apps to run on it, up to 64Gb of CF/SDHC storage, wifi, and so on.) Oh, and the killer? iPaq and keyboard weigh 350 grams -- same as the Pomera DM10 -- and fold down to the same size.
Upshot: unless you absolutely need the ability to type non-stop on something that fits in your pocket and runs for 20 hours on AAA cells, a (mutter, grumble, why can't Apple make a competitor?) Pocket PC is way better value for money. And if you need the battery life, spare iPaq batteries are commoner than hens' teeth.