Brendan O'Connor created a small applet that allows exploring the beta distribution interactively (just hit arrow keys on the keyboard):
This is a good example of what interactive visualization can do - Andreas Buja was also showing some cool examples some time ago.
He also has source available (for Processing).
The biggest thing I learned is that the conventional order of parameters in the Beta(a,b) notation is reversed. When 'a' goes up, the density distribution shifts right. I never noticed this except it's really confusing if you're trying to use the keyboard to control it.