Tables were originally meant only to display tabular data. Then once people started getting interested in making websites look good they started using tables as sort of a workaround to help make the layout visually appealing.
Today we have a better and much more efficient way of doing this. It is formally known as Cascading Style Sheets, but it's friends call it CSS.
Let me count the ways.
Using tables combines your presentation with your content. These do not mix well. Combining presentation and content creates large files that the viewer has to download with every page. This means that the pages will load slowly and your site will be more expensive to host.
Another problem with using tables is that when the time comes to redesign your site it will be very time consuming. (And time consuming = expensive) However when redesigning a site that was laid out using CSS, the content doesn't need to be touched at all. All you need to do is edit the style sheets for a fresh new look! This makes it quick and easy to keep all of the pages of your site looking consistent.
Another disadvantage to using tables is that table based pages do not translate well to those viewing your site through different types of mediums such as on a cell phone or BlackBerry. This means your content is not device-independent. Table based layouts also present a problem to those with disabilities, such as those that listen to the web.
Using CSS for the presentation of your site means you will use more semantic markup. This greatly helps with your search engine optimization.
More Information on CSS vs. Tables: