Ask 10 web designers that quuestion and you'll get as many answers - possibly even more !
I design to 1024x768 as a standard, as does every other professional web designer I currently know. I make everything I do fluid though, and I also test thoroughly at 800x600, so I guess you could say that even though I'm going for the higher resolution as my standard ball-park, I ensure backward compatibilty too.
It's a thorny issue and you'll never get a concrete answer.
The server logs from some of my sites indicate that above 95% of my visitors have 1024x768 or greater resolution, while other sites I have enjoy an almost even split between 800x600 and 1024x768. This depends on the nature of the site content - the more technical sites invariably attract a higher resolution visitor, but also keep in mind the standard monitor sizes offered with computers these past couple of years, which have all been capable of 1024x768. Capability does not mean that all computer users will actually run their PC at that resolution though. Many prefer 800x600.
The best advice I can offer is to go for 1024x768 but use percentage table or CSS controlled widths and images less than about 700 pixels wide (maximum) with top navigation links or choose an image width including a side navigation panel that can cope with an 800x600 resolution.
Another solution I have used in the past is to create two sites or use dynamic management, where the first page of your site contains a browser sniffer to detect screen resolution and forwards the visitor to the relevant pages. You can autiomate this or simply offer 'Click here for 1024x768' and 'Click here for 800x600' hyperlinks.
I'm rather fond of using PHP to manage this, where the source images are high resolution and the web page(s) are filled with PHP controlled images where the image size and resolution is dynamically generated at the web server to fill the page at a given size.
Like I said, "Ask 10 web designers.... "