At the 'Main' menu place the red arrow cursor next to 'Play Movie' and press the 'Up' arrow key on your remote control. The red arrow cursor will then disappear and if you press 'Enter' you will be able to view the full Ring tape.
The evil tape that kills you in 7 days isn't accessible to watch anywhere on the DVD, right? WRONG!
The selection "Don't Watch This" is not the tape, but the deleted scenes from the movie. So where can you watch the tape. Go to the main menu. Highlight 'Play Movie'.
Once here, press Up or 6 on your remote and the red arrow cursor should become invisible. Hmmmmmm. Press the Enter or Select button on your remote to start the movie. Afterwards, the menu will appear without all of the cool voices and sound effects and a telephone will ring twice.
P.S. I found this cheat by accident on my computer by moving the mouse over the chair on the title screen!