If you're looking for a continuous rotation potentiometer, or you're looking to measure the number of turns of an axle or spindle, consider Rotary encoders. Rotary encoders measure rotation about an axis by producing a series of pulses as the shaft rotates. The more pulses produced per roration, the higher the resolution of the encoder. A typical encoder will give you 128 or 256 positions around a circle.

Some encoders are relative or incremental, meaning that they don't give you an absolute position, they just tell you when the shaft has rotated to the next measurable position. Some encoders offer direction, and others don't.

Some encoders have detents, meaning that there's a little stop at each position around the encoder. These encoders don't turn as smoothly as continuous encoders, but they do make it easier for a person turning the knob to know how far they've turned, by counting the detents.

Encoders can be optical, meaning that they measure the rotation by measuring the light-dark transitions of a striped shaft using a photodiode, or contacting, meaning that they measure rotation by counting passing contact bumps. The former tend to be smoother and wear out less, but are often more expensive.

Many encoders need to be used with a quadrature encoder. A quadrature encoder listens for the sequence of pulses on four pins of the encoder to tell you whether the shaft is rotating clockwise or counterclockwise. Bourns makes a number of good encoders.

Chris Cummings offers the following advice:
"You don't need to spend more than $50 to get one that is guaranteed for several million cycles, unless you're opening a space shuttle cargo bay door or you need it to operate while immersed in acid or something. Do not spend less than $10 or you won't be satisfied. The big difference in quality comes between models with plastic shafts and stainless steel shafts (get stainless steel!). They all work pretty much the same way aside from that."

Grayhill also makes a nice encoder, Digikey part number GH3064-ND.

US Digital sells a variety of electronic parts, including the S4 rotary encoder, recomended by James Powderly as a simple and effective rotary encoder.

Thanks to James Powderly, Jonah Brucker-Cohen, Chris Cummings, and Taku Lippitt for the links.