All webtv units, at least according to the official web page, run a MIPS 64-bit RISC processor, but only have a 32 bit bus. I've been doing some digging on this, but haven't quite talked my uncle out of his yet so haven't looked inside.
However, there are various ports of both Linux and NetBSD to the MIPS platform, and possibly OpenBSD as well (not sure). The only problem I see with the webtv unit is the fact that MIPS licenses the core to other companies, so each manufacturer's processor is slightly different. Registers are moved around, etc. The MIPS processor in the webtv is done by QED (http://www.qedinc.com), and there is no code for this particular version of the MIPS processor in any of the source trees I've looked at. It may not be necessary, as QED claims that their processor is pretty much a R4700, which is supported; just something to be aware of.
If anyone is interested in pursuing this further, the following links may be of help:
http://www.webtv.com the obvious place to start
http://www.netbsd.org/Ports/hpcmips geared towards MIPS based hpc/pdas, but should be about the same
http://www.netbsd.org/Ports/newsmips Sony MIPS based network stations
http://www.fnet.fr/linux%2Dmips MIPS Linux pages
http://decstation.unix-ag.org Port of Linux to several older MIPS-based DECstations
Note that none of these probably supports webtv out of the box, but should give a general feel for the possibilities. Also, I doubt much work would be needed, if any, at least on the hpc netBSD port, as most winCE devices are about the same, IMHO.