To make the Phillips DVP5960, my latest toy, ignore region encoding, simply follow these steps:

1. Turn the player on and open the tray
2. Press "Setup" on the remote
3. Go right until you get to the "Preferences" page
4. Enter 138931 using the remote. The region code will appear
5. Use the up and down buttons to select region, or 0 for region free
6. Press "Setup" then "OK" on the remote

That should be it. Thanks to everyone whose comments appear on the Google results page for the search terms "phillips dvp5960 region hack"!