What are some ways I can extend the functionality of an Xbox 360?

Unfortunately, the current answer is: nothing, really. You've got http://en.wikipedia.org/wiki/Microsoft_XNA for Microsoft-approved development and http://creators.xna.com/en-US/ for officially supported homebrew stuff. The only thing that modding does currently is bypass the copy protection allowing you to play burned games. Everything else is actually easier to do on an un-modded machine. The original Xbox, on the other hand, has exploits to allow arbitrary unsigned code execution--allowing for a much broader range of available benefits from modding, including http://www.xbox-linux.org/wiki/Main_Page, http://xbmc.org, and the like. Perhaps someday the 360 will be reverse-engineered to this extent, but not yet. You can check out http://free60.org if you're interested in the bleeding edge of 360 homebrew, but there's not much interesting going on there yet unless you're a diehard kernel hacker that gets a kick out of running Linux on anything that blinks. :)

Having been out of the loop for a couple years, I just read through a big chunk of the free60 wiki in hopes that they'd gotten their shit together. I don't think you're going to like it very much. It requires soldering to the 360's motherboard, building JTAG and SPI interfaces for your computer's parallel port, and a lot of tedious kernel cross-compiling. And the result is a painfully slow and basic linux kernel supporting roughly none of the hardware available on the 360 with any reliability. There is no 3D or 2D acceleration, and apparently most framebuffer applications give garbled output. And all of this is only possible if you have one of a couple specific firmware versions from before summer 2009. Even if I got a 360 for free, I still wouldn't go through that the pain. If you're not a linux hacker, and the idea of a locked-down computer doesn't literally infuriate you, there's nothing there for you. And free60 is pretty much the only 360 hacking project I've ever heard of. The 360 is really, really not hacker friendly. This on top of the fact that the 360 isn't a very interesting system in the first place--you can build a functionally identical computer for a couple hundred bucks. Or you you could just buy an old quad-core G5 Mac with a $50 ATI graphics card and have an even better, but still similar, machine.

Apparently they're working on a de-banning hack. Get it unbanned, reload the original firmware, sell it, profit!

Apparently they're working on a de-banning hack. Get it unbanned, reload the original firmware, sell it, profit! It's going to be about as ethical as credit card scamming, though. Each XBox has an electronic ID. While Microsoft clearly isn't telling, it's likely that the ban is targeted against that EID. To circumvent the ban, you'd need to forge a clean ID. A clean ID that might belong to a 12 year old cancer victim's XBox in Duluth.

Nothing, except built-in offline features. Media Center extender or Media streamer on another TV?(extra codecs via transcoding).

Banned 360's also now lose the ability to be a Media Center extender, as well as saving games to the HDD (when they get flagged, they also disable features locally offline). Also, any profile or save game from the banned 360 will show as corrupted when opened on a non-banned 360; so you can't even use them for playing for achievements offline and then bring them over to your unbanned 360. MS really have gone to great lengths to make banned 360s a near paperweight. There are reports with the latest banning wave that people who never modded their console have also had it banned, so its not like legitimate users of the service aren't also at risk of getting their system effectively bricked. So basically all you can do with a banned 360 at this point is play offline games on it off the DVD (legit or otherwise) with a local profile and save games that are not transferable.