You can animate bezier curves using shape keys. Add a curve and in edit mode, press I to add a key and select curve. Tab into object mode and then back into edit mode. Make changes to the curve press I to add another curve key - tab to object mode and back into edit mode. Continue this for all your keys. In object mode select the curve go to the IPO window, select shape and you will see a list of keys on the right side. Select the base key - the first one with the dashes and then control left click at the 0 axis intersection to add a speed curve; control left click to add another point and then move it up on the Y axis. Then for some reason nothing happens if you play the animation. To get it to work go to the editing (F9) panel in the buttons window and in the Curves and Surfaces panel de-select Relative Keys. Now it should work.
Alan
Dude! This thread saved my life. I needed to animate using curves to modify
a plane with a logo on it. I was going crazy trying to figure how to make it work
with keyframes. I still couldn’t get shape keys to work with the curve consistantly
(which means it worked and didn’t work, but I had no idea why) so I ended up
using hooks.