Tables are there to present tabular data, not to layout your screen. They were used that way because there was no alternative. Now that CSS is available - and pretty well standardized across browsers - there's no reason to use tables to layout your screen. Besides that, think of how difficult it is to add a piece of information to the middle of your screen with tables, compared to a CSS layout - a far more common operation than a complete redesign (which is also easier with CSS).
If you want to know why, go to a website laid out with tables and turn on your screen reader. Then do the same thing with a well-designed page of CSS. Besides the accessibility issues, tables use far more markup, which creates (much) larger files that need to be downloaded, costing you bandwidth and slower loading times.
To see some of the magic of CSS, check out
css Zen Garden: The Beauty in CSS Design. It will blow you away.