Sitting on top of my VCR is my new special Apex DVD player. This puppy has the hidden menu and everything. I don't have any non-region-1 discs to test it with, though I'll probably order Eyes Wide Shut from Amazon.co.uk sometime soon. I couldn't get a CD-R of MP3s I made to work with my first try--though I suspect it was the way I made it that's tripping up the player. I played a DVD in it too, of course, and that worked just fine. (So much better than VHS! So much!) My only complaint so far is that it seems to obliterate what little reception I get of 4 of my 7 TV channels, but who needs TV when you have DVDs?
If you want one with the hidden menu, they're going for about $300 on eBay, and prices continue to go up as supplies dwindle. I bought mine from Oobgarm, who still has a bunch left. (He offered to sell me one off auction for $320, I'm sure he'd do the same for you.)
Of course, if you don't need the ability to change the region code or disable Macromedia copy protection (and who does?), you will always be able to get a new one at Circuit City for $180. You get the MP3 functionality, as well as Karaoke! (It even has mic jacks on the front!) It plays DVDs, too.