Many low cost "WiFi card reader" devices (which make a spiffy off-the-grid, LAN-in-your-pocket) support WebDAV as well as SMB/CIFS. Sadly the end-user docs often don't mention it though.
Amazon sells the discontinued Sony WG-C10 for $20 to $23 USD right now and you can plug in an SD card or USB flash drive. When up and connected these expose WebDAV on port 8081, user=admin, pw=admin (at least when the firmware has been updated, I didn't test out of the box). Other similar devices like the Verbatim MediaShare Wireless also claim WebDAV support.
These can be useful in and of themselves, but they also make a cheap WebDAV server development testbed.