This is a really cool interactive applet for demonstrating Newton's Method.
http://www.math.umn.edu/~garrett/qy/Newton.html

And here is one from the same website that shows a 'pathelogical' case, where the iterations don't converge on the nearest solution:
http://www.math.umn.edu/~garrett/qy/BadNewton.html

And here are six animated gifs that illustrate Newton's Method. Not interactive, but very nice nonetheless:
http://math.fullerton.edu/mathews/a2001/Animations/RootFinding/NewtonMet...

The above animations are part of a website that shows animations of a variety of iterative methods of finding zeros:
http://math.fullerton.edu/mathews/a2001/Animations/RootFinding/RootFindi...