The Chumby is an embedded appliance that runs Linux. It runs Flash Lite 3 (though I'm sure it can be hacked to run other things) which is close to Flash Player 7 and only supports ActionScript version 2. The latest version of Adobe Flex cannot be used to develop stuff for it; you need to use Flash. Supposedly, there's some open source tools too, but I haven't looked into them.
You can now buy a Chumby One for $99, which has a faster processor than the original Chumby. Grrr. This came out exactly one week after I received my $139 Chumby Guts.
The touch screen is so-so; it's not as good as the iPhone's. Use images or touch areas of at least 48x48 for best results. The fonts too aren't as sharp as one might like (probably because of the large, but relatively low-resolution (QVGA), screen), but I haven't (yet) figured out which ones look the best. It can stream MP3s over the internet using a direct URL, but has a problem with non-standard sampling rates. Stick to a multiple of 11.025 kHz. If you ignore this advice, you might end up with chipmunked audio. There's no way (as far as I can tell) to persist state locally (something about security, I suppose), but you can set configuration information using a Chumby configuration widget. There's a good example of one such widget here.
Here's some useful links for developers:
This project is open source, so please contribute to it.