Set the backlight to 'Always On'.

This is not an ideal solution for everybody as it will eat the battery but this is perfect (and possibly as designed for powered docking systems where you really would want the current song information displayed.

Sorry if this was already known but I have just got back to the UK from San Francisco where I bought my new 80GB silver. The Apple Store attendant did not know the answer but after 5 minutes of playing around with the display model I confirmed that this solution works and there do seem to be people on here who want to turn it off. I've been dying for internet access to post this ever since.

I do not have a solution that does not use the backlight but that may come in a future update. To be honest though with the backlight off you won't be able to read the screen anyway IMHO.