The research I found at
Browser News (granted, it was from one site and the stats are probably different depending on who collects the data and when the data was collected) indicates that about 3% of people use 256-color displays. Unfortunately, an additional 5-6% of users use the AOL browser - most of them in the default 8-bit compression mode which uses 256 colors. The BrowserNews website indicates that "the bottom line is that although the number of those with 8-bit displays is small and shrinking, design for 256 colors will remain a serious issue so long as AOL continues to compress (mutilate) images."
Even so, I deliberately chose NOT to design with only websafe colors. I am debating whether having a pop-up "alert" telling AOL users that their browser is munging my images or not. I get the feeling that sort of thing is generally frowned upon in the web development community, but AOL really pisses me off!

(See my thread when I first discovered that
here.)
I remember reading somewhere (perhaps lynda.com?) that designing for 256 colors was not as important today as it once was. I supposed if you're concerned about how AOL users view your site, then you should still design with the websafe colors in mind. But, my feeling is that AOL is going to make all my photos look bad anyway - regardless of whether I use the websafe colors for my site or not, so what's the point of worrying about it?
Jeanie