Python - animation with matplotlib.pyplot

Question

How can one create animated diagrams using popular matplotlib library? I am particularly interested in animated gifs.

Answer 1

Update in 2017

Matplotlib has the animation module, and in it you find the ImageMagickFileWriter class. It is advertised as "File-based animated gif writer."

Documentation: http://matplotlib.org/api/_as_gen/matplotlib.animation.ImageMagickFileWriter.html#matplotlib.animation.ImageMagickFileWriter