DSi hacking?

There are tons of small, electronic devices that are lower-spec than DSi's that also happen to be more expensive than DSi's, so I was wondering if there was a community somewhere that got a DSi to do neat tricks like booting to Linux, working as an Electronic Dictionary, or similarly cool tricks.

There were plenty 3rd party of cartridges available for the DS that could take an and SD card and you could load games onto. They were mainly used for pirated games but they could also be used for homebrew. Not sure if they will work with the DSi because I imagine that Nintendo would have beefed up their anti-piracy measures with that, but you might sill be able to use it in DS mode. 

This one claims to work with the DSi, but you would have to do some research to confirm this. 

http://www.cyclopsds.com/cgi-bin/cyclods/engine.pl

As I said, there was loads of homebrew out there for it, including a Linux port: http://www.dslinux.org/

there is no native DSi software that I'm aware of, 
but it can run ds homebrew and emulators.
you would need a flash cart. I think DS linux works, but you can't use the extra ram from the dsi, and you can't use the ds ram expansion. 

To run all this you will need a DSi compatible flash cart,  and some apps to run on it.
you can find some apps here:
http://filetrip.net/nds-downloads/applications/
(that domain contains no DS roms) 

Not having the added hardware features of the DSi is the drawback of using the DS stuff, though.  Is there really nothing out there for getting into the DSi and having full access to the memory, camera, etc.?

Well, I managed to dig up this photoset on Flickr.  So... I think knowledge is out there.  I'll keep looking.  http://www.flickr.com/photos/micahdowty/sets/72157621023570420/

Yeah, that site looks like a few XBox 360 emulator sites I've seen.  I'm inclined not to trust it based on the simple fact that they never even show what the flash cart looks like and it seems that some of their "retailer" pages are down.

Oh, they're legit. I own one of their older flash carts for my DS, so I know they were at one point.