On current browsers, the entire table must be downloaded and the dimensions of everything in the table must to be known before the table can be rendered. That can delay the rendering of your content, especially if your table contains images without HEIGHT or WIDTH attributes. 
If any of your table's content is too wide for the available display area, then the table stretches to accomodate the oversized content. The rest of the content then adjusts to fit the oversized table rather than fitting the available display area. This can force your readers to scroll horizontally to read your content, or can cause printed versions to be cropped. 
For readers whose displays are narrower than the author anticipated, fixed-width tables cause the same problems as other oversized tables. For readers whose displays are wider than the author anticipated, fixed-width tables cause extremely wide margins, wasting much of the display area. For readers who need larger fonts, fixed-width tables can cause the content to be displayed in short choppy lines of only a few words each. 
Many browsers are especially sensitive to invalid syntax when tables are involved. Correct syntax is especially critical. Even with correct syntax, nested tables may not display correctly in older versions of Netscape Navigator. 
Some browsers ignore tables, or can be configured to ignore tables. These browsers will ignore any layout you've created with tables. Also, search engines ignore tables. Some search engines use the text at the beginning of a document to summarize it when it appears in search results, and some index only the first n bytes of a document. When tables are used for layout, the beginning of a document often contains many navigation links that appear before than actual content. 
Many versions of Navigator have problems linking to named anchors when they are inside a table that uses the ALIGN attribute. These browsers seem to associate the named anchor with the top of the table, rather than with the content of the anchor. You can avoid this problem by not using the ALIGN attribute on your tables. 
If you use tables for layout, you can still minimize the related problems with careful markup. Avoid placing wide images, PRE elements with long lines, long URLs, or other wide content inside tables. Rather than a single full-page layout table, use several independent tables. For example, you could use a table to lay out a navigation bar at the top/bottom of the page, and leave the main content completely outside any layout tables.