For websites I've set my lowest requirements like this:

800x600x16, at least IE6 supported (maybe with unimportant flaws). Netscape 4 is not supported at all, Netscape6 untested, Netscape7, Mozilla 1.5 operating fine.
Opera9, Firefox2, IE7, Chrome are a must.

800x600 is still interesting for web TV, certain console browsers, webbooks and the like.
For the desktop PC this resolution is dying out and can be ignored soon.

But I agree with ello that some border around the main website is a good design element. This is why I stay at 800x600 for now.