Back in the day, 800 x 600 was the screen resolution to design for - and maybe 640 x 480. Then along came 1024 x 768, etc, etc, etc.
But then it gets worse: now we have
This is a common but complex question, which unfortunately does not have a single best solution. It all depends on the kind of content that you have. You can use a fluid layout, or design your site differently for different resolutions (see http://www.maxdesign.com.au/articles/resolution/). For an example of a fluid design, check this out - http://hicksdesign.co.uk/journal/finally-a-fluid-hicksdesign