XBMC is one of the best uses for an old xbox, as long as your not interested in HD content it will play nearly anything. Installing Linux on one is possible as long as you don't have the 1.6/1.6b revision as no one ever managed to fix an overscan issues with the display chip. It isn't too hard to do but as Geffen said it is terribly slow as it only have a 700 Mhz CPU and 64MB RAM, not something you could comfortable browse the modern web with. The PS3 and Wii both have web browsers that are better suited to that.
If you can't find a converter you could always pick up a USB hub (£1) from the pound shops and an old gamepad and join the cables. The ports on the Xbox are all USB so you can attach a hub to them without any problem. This gives you 4 USB ports for keyboards, mice and memory sticks etc.
I am in the process of migrating away from the Xbox now as I have a HDTV and want something with a higher resolution. I have an EeeBox (ASUS EeePC in a box) which is an ideal replacement and uses about 20W idle (less than the Xbox). I have modded the IR dongle from the xbox to USB so I can still use the xbox remote to control it (
see the bottom of this thread). I am undecided on the software at the moment, XBMC runs fine on it under Windows but the hardware support is nonexistant at the moment which means all the decoding is pushed to the tiny little Atom CPU and not offloaded to the GPU. I feel this is due to it being an early project on the Windows platform, I'm sure it will change over time though. MediaPortal (was a fork of XBMC) on the otherhand does do hardware support (it offloads the work to WMP).
Boxee (also a fork of XBMC) looks to be an interesting project but there is no Windows version yet and I don't know what the hardware requirements are going to be like.