Mandelbrot Set

I like this video. (Note that the song has some foul language here and there. But it too still has some nice points.) Wikipedia has some nice articles on the fractals mentioned, although I can't guarantee accuracy of all details (the first is from a different website, though, which has a nice applet showing the construction of the Peano Curve):

Peano Space-Filling Curve
Koch Curve
Cantor Ternary Set
Sierpinski Gasket
Mandelbrot Set
Julia Set