I have a number of static figures that I use for illustrating how prior beliefs influence inferences in a Bayesian context, and I have the nice Bayesian Coin Tosser that my colleague Paul Lewis wrote that shows what happens for a single observer given a particular prior. But this is the nicest visualization I've seen yet. It's from Corey Chivers (bayesianbiologist). It illustrates how two observers with different prior beliefs about the frequency of heads (p=1/6, variance=5/(36*13) vs. p=8/11, variance=24/(121*12)) converge to the same posterior density as the number of observations increases. He also provides the code (in R) to produce the animation.
This shows very nicely that if you have a reasonable amount of data, it makes little difference what your prior is.1