I have recently come into posssession of an LG V181 combo VCR and DVD player. It’s fun! and exciting! and not very expensive!
Amazingly (considering the price) it does quite a good job dealing with DivX and Xvid files. The only problems I’ve found are with high bitrates, where it (unsurprisingly) struggles, and with a memory leak that seems to occasionally hit long files, causing the audio to fall out of sync.
And thanks to this thread I found the means to make it region-free: open the disc tray, press 0000, and disable the region lock by pressing 0 again.
Unrelatedly: yay Russia for winning their first Hopman Cup! But boo to the official Web site, which still hasn’t been updated with the news.