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zooloo's right - it would seem that you are setting your layout to have an absolute width (eg: 1000px). Setting it to a relative width (100%) will make the content use the available space.
This is known as a fluid layout. The CSS Forum [webmasterworld.com] has a number of threads dealing with creating this type of layout using CSS.
the only solution is to make sure your total width is around 725px or less. note that with 800x600, the 800 width doesn't account for actual viewing area which varies with different monitor brands. you also have to factor in browser window borders and right scroll bars. and if your visitors are predominantly AOL users, 700px width is probably a safer bet.
have you examined your web traffic logs to determine just how many visitors are actually accessing your site using 800x600 resolution? if the number is neglible, I wouldn't even worry about changing it, especially if it's only one page. just make sure all your important content is visble in front of the scroll.