Another reason for using ems instead of pixels for text is that in IE6 and under you cannot resize pixel based test via the browser controls. You can use relative sizes for the fonts and pixel sizes for the containers but be aware that the design won't scale uniformly. However, if the site is otherwise well designed it may not be an issue and many people do it this way.
Designing a whole site in ems is more complicated and time consuming than using pixels as there are certain issues to overcome. It all depends on the job in hand and how you want your page to look when resized. If using pixels for the layout (ems for text) then as long as the page is still readable after a few text resizes then that's ok as it will never be perfect anyway.
When using ems for the layout then the whole page scales together and still looks the same more or less.
I use ems too and for the same reasons that Paul outlined above. From a usage point of view there are a couple of exceptions. To set the base size of my website text, I use the t-shirt sizes, usually medium. I'm pretty sure you can then use ems indiscriminately, but I've always been nervous sizing text based on a unit that depends on a the size of a text character. That sounds awfully circular to me so I use percentages to handle font-sizes for heading, etc. That keeps everything relative to the base font size. Then all my divs, margins, indents, everything I do in ems. It's identical to doing it in pixels, just with a different unit of length. A unit that scales well and keeps your page elements in the same ratio. It's an effect that seems to hold a layout together, the way you designed it, better than any other technique that I've worked with.
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