Assuming a fluid layout is not an option (since that is a different discussion all together), what is the recommended width for a site layout? What are the pros and cons of different sizes?
If you use a fixed width that is any wider than the smallest screen likely to visit your site, you will annoy and frustrate users who have to scroll sideways to get to the rest of your content.
At one time it was 800px; however, more and more sites are beginning to use 1000px. This is driven by the fact that, more often than not, visitors' low end resolutions are at 1024x768. The additional 24 pixels leaves room for the browser chrome, padding and margins you may want to manipulate, etc.
Just to give some perspective, even the new wave of netbooks with their tiny screen have resolutions of 1024x768.
But, above all else, know your audience as @warren suggests and capitalize on that.
According to these statistics, a minimum of 1024 pixels wide will cover most users.
I've always kept with 960px as it's viewable on 1024x768, and is cleanly divisible by 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320 and 480... so I can split up the design of my site (using the rule of thirds) cleanly.
Check out http://browsersize.com for some quick stats on screen resolutions users use nowadays. You can use http://setmy.browsersize.com to quickly resize your browser to emulate viewing your website at a particular screen resolution. Make sure that your layout satisfies at least the most widely used screen resolution (1024 x 768).
Also, don't necessarily aim to take up the maximum horizontal space. The width of text (number of words per line) ideally shouldn't exceed a certain threshold for usability:
At the very common 1024×768 screen resolution, most fixed-layout websites don’t use all available space to the left and right of their content. Flexible layouts make a better use of horizontal space, but struggle to maintain usable line-lengths. Usability experts have told us that there are just so many words you should put on a line. Between 8 and 12 words seems to be the ideal line length. Print media, especially newspapers, don’t hesitate to use even shorter lines. Why? Because they can, by laying out text across several columns.
I also use a layout between 950 and 980px and always centered unless the client demands otherwise :)