I immediately went to manybooks.net and downloaded a couple dozen literary classics (Candide, Metamorphosis, Ulysses, etc.), all free. I also transferred a couple dozen philosophy PDFs that I've been meaning to read.
Unfortunately, one of these was a scanned-image pdf (JSTOR style), which didn't transfer at all well. The Kindle shrinks images to fit, so I could barely make out the words. So much for JSTOR. [Update: fixed!] But I was relieved to find that the others (including ordinary text-based PDFs) convert and display
Other than that, I have no serious complaints. I find the Kindle very pleasant and comfortable to read from -- the main selling point is, after all, its ink-based display technology -- there's no glare, so it feels like reading a book, unlike backlit computer screens. (Minor aesthetic complaint: the background is a newspaperish gray rather than pure white.) It's small, light, and easy to hold. Some people complain that it's too easy to accidentally bump the 'next page' button, but I haven't found this a problem myself, so long as I put it to sleep when carrying rather than reading it.
I like the navigation a lot. It's actually quicker and easier than turning a page in a regular book. Granted, you can't flick through multiple pages nearly so well, but there is a 'search' feature which more than compensates for this. Other options allow you to 'highlight' text, 'add notes', or 'bookmark' pages for future reference. And you don't need to worry about losing your place, since whenever you open a document, it picks up from wherever you previously left off. (I should note that the tiny keyboard is made for thumbing, not typing, so you won't be writing treatises in the margins. But it's handy enough for jotting down quick thoughts as you read.)
Aside from comfortably reading e-books and online papers, the other great feature of the Kindle is free mobile internet. The display is a bit awkward, and - combined with the clunky little keyboard - you certainly wouldn't want to use it as your primary form of internet access. But it's nice to have access to email on the go, and my feed reader (bloglines) works tolerably well on it, too. (I'm sure the iPhone is much better in these respects, but I'm deterred by the price tag.)
[Update: it turns out I hardly ever use the Kindle's internet access -- it's just too slow and clunky. But note that you can use free services like Kindlefeeder.com (from your home computer) to convert rss/atom feeds to kindle format, and even automatically deliver the converted feeds to your kindle. See 'Read Anything on Kindle' for more detail.]
Other features are fun but superficial. There's an mp3 player, but the sound quality isn't great. There's a (black-and-white) picture viewer, and it's nice to be able to carry around photos of loved ones, but the resolution is far from photo-quality. I hear you can even play Minesweeper, but I fortunately haven't gotten that bored of reading yet!
Is it worth $399? It is for me, though it may not be for everybody. There's a lot of free digital content out there that I can now take full advantage of. In particular, my main reason for buying the Kindle was to read online philosophy papers, which it's great for. But now that I've got it, I find that I'm also appreciating the opportunity to read all those old literary classics that I wouldn't otherwise have gotten around to. I don't expect to buy much paid content from the Kindle store, since I don't tend to buy much of anything, but you might want to compare prices if you're into that kind of thing. (I gather the Kindle versions tend to be slightly cheaper than hardcopies, and they're conveniently "delivered" wirelessly to your device in minutes.) At present, selection seems to be limited mostly to new bestsellers and old public domain works. So be warned: anything in between may not be available.
Full disclosure: Amazon will give me a 10% referral fee if you buy it via this link!