When I log in, this is what I see:

So right away, that's some pretty good info. And you can break that down in graph form.

But Sitemeter also pulls information about my individual visitors. Like, crazy amounts of data. Like what monitor resolution they have. (I can actually see how this would be helpful, depending on what you're trying to do with your site; you could scale your design up or down to fit the majority of your viewers' monitors.)
Also, you can pull up a world map that shows where all your visitors come from. This is the most fun part.

The cursor disappeared when I took the screenshot, but what's happening is that I'm mousing over a little green dot on the eastern edge of China, which causes a white box to pop up with the viewer's server and location.
So if I click on that visitor from T'ai-pei, I discover that he found this old post on a Google search for "something told the wild geese" (OK, wow, that post is the #1 hit for that search in Google Taiwan!) and stayed for 0 seconds. Guess he didn't find what he was looking for. Also, he was using IE 7.0 on a Windows NT machine.
Anyway, that's Sitemeter. Can you see why I love it so far?
UPDATE. Sorry, I forgot to mention my one problem with Sitemeter: as far as I know, it doesn't track RSS subscribers. (Or if it does, it doesn't distinguish them from regular visitors.) Anyone know more about this?