Fixed width web sites are good when your content is formated a specific way and you want it to be displayed that way.  For example, if you have forms where the descriptive text and response areas should be in just the right location.  Or if you have images that you want to have the text fit just so around it, a fixed site would be better.

A variable width site is good when most of your content is text or you are not concerned too much with how the content flows within the windows.  The browser will automatically do a best fit for the content.