Yes, GeoGebra supports animation. In fact, this feature is built-in and explained on the Wiki page provided for customers. To add animation to a free number, angle or a dependent point, then right click on the item and select Animation on from the Context menu. To change the way items animate, simply change their properties in the Properties window.
To control the animation manually, press the following keys:
Shift + arrow key gives you a step width of 0.1 units
Ctrl + arrow key gives you a step width of 10 units
Alt + arrow key gives you a step width of 100 units
