It depends on the site. Many people create sites this way, and it certainly helps in terms of getting a basic layout.
The main problem I find is that the layout becomes too 'static'. In other words, sites might work well at one resolution, but at higher resolutions, there'll be a lot of blank space outside the page, and at lower resolutions (or smaller browser windows), part of the design might get cut off. Also, if you add HTML text into certain areas, some people with poor sight might force the text to enlarge and this might break the layout up.
Personally, I would use Photoshop & Imageready or Fireworks to create an 'ideal' layout, then I go through the HTML and make some parts of the table 'flexible'. For example, an area of flat color would become a single cell that doesn't have a fixed width/height. It's not easy, though, sometimes requiring a lot of trial and error, and certainly requiring a lot of testing in different browsers.
Having said all that, some layouts work quite well at a fixed size, and if that's the route you want to take, just be sure to fix the font sizes throughout.