A knob that can be turned by hand, have the position read, and turned by software to another position? I'd like to be able to change variables on the Arduino by adjusting a set of knobs.  When I get to a desirable setting I'd like to be able to save those settings on the Arduino... and then I'd like to be able to load those settings back, and have the knobs turn themselves back to the correct positions.  Specifically I'm thinking of using this with a synthesizer.

I understand how to do all of this, except, I don't know if there are knobs that allow this type of behavior.
If you attach a knob to the Analog Feedback Micro Servo, either directly or via gears, then you can use the pot output to measure the current position and use the normal servo control protocol to turn it under software control.