I'd stick to 800 because many people (around 33%) have a 800x600 resolution. Go to:
http://www.w3schools.com/browsers/browsers_stats.asp and scroll down to display resolution to see the stats. 800 will look fine to someone who uses higher and most do, but greater than 800 will generally not look good to someone using a 800x600 resolution.
EDIT: Oops, I'm sorry. I'd actually go a tad under 800 (760?) because you have to take the scrollbar into consideration. To see what I'm talking about, create a simple black jpg 800 pixels wide. Change your display resolution to 800x600. Use your browser to open it up and you'll see that a horizontal scrollbar appears (or your browser might automatically shrink it to screen size, which won't happen in a site unless the web designer shrinks it which might look bad, so click on it to bring it to regular size). You generally don't want to make your viewers scroll right.