Ton-
There are any number of reasons that people might choose one over the other.

For me, the best reason to pick fixed width is to insure dynamic content (text) always looks as expected.  Using "full width", if you do not specify a width for a paragraph of text then that paragraph may stretch across the screen as a single line under high resolutions.  Text is usually easier to read if it does not stretch too far from left-to-right.  

From a graphic design standpoint, variable-width pages ("full width") can be a nightmare when you're trying to present content in a particular way.  You could define fixed widths for individual pieces of content, but if you get to a point where you have to do that it's usually easier to just go with a fixed-width skin to start with.

On the other hand, if you need to show a lot of content at once (say, a big table of data) the more screen space you have the better since you'll cut down on scrolling.

I tend to go for fixed-width because I've had too many pages look awful when I allowed the content to dynamically span under 1600x1200 resolution.

-mamlin

Ditto re: mamlin and Andrew

Plus another reason for fixed width is more flexibility in defining skins and containers without the use of tables. Although it can be done, it's pretty hard to get a skin that is completely CSS driven without tables to work in a full width skin.