I ran across this today and found it interesting. Do you see the dancer spinning clockwise or counter-clockwise? According news.com.au, you use more of the right side of your brain if you see the dancer spinning clockwise.
Personally, I first saw the dancer spinning counter-clockwise (no big surprise there), but by looking away and back again, I can see her spinning in either direction now. Although, try as I might, I can't see her change direction while looking at her.
Update: The animated dancer illustrates an interesting browser difference. In Internet Explorer, the dancer moves jerkily, leaves blips on the screen, and consumes an inordinate amount of memory. Firefox, on the other hand, displays a smooth animation with no blips and only uses 20%-25% of memory compared to IE.