DLink makes a Network Controller which includes 2 USB-2 ports an ethernet port, and runs Linux with a Web interface. It usually sells for around $99.
Netgear makes a "WiFi Storage Router" which includes 1 USB-2 port, 1 WAN port, 4 LAN ports, and the WiFi radio. I saw this on sale at CompUSA for $49.
Both offer source code for their Linux kernel in case you want to cook up a kernel that is a bit more "juicy".
There was another "smallest computer" candidate, which looked like an oversized RJ45 connector, which had ethernet on one side and serial port out the other side.
In each of these cases, the flash RAM can be flashed to start a boot-loader which can then boot from a USB or LAN drive. After that, the only limitation is the RAM and how it's flashed. Flash RAM can be run in "cached" mode which makes it more like static ram. It would be slow, but could function as an X-client instead of a web server interface (which is the default interface provided).