What do you call the component that works like a potentiometer but has no stop in either end. The eternal sort that can be used to alter a value of something in the negative direction by turning counter-clockwise and the opposite turning it the other way?
While they often provide a knob, like the potentiometers used on control panels do, that's where the similarity ends; a potentiometer outputs a resistance that varies based on the position of the knob. A rotary encoder has two pins (and ground) which you pull up to Vcc (5v on most arduino), and which are grounded by the encoder depending on it's position; your sketch monitors these pins and you can deduce the direction of motion from the pattern in which these two pins go low. You interface with them in a completely different manner. There are many guides and tutorials to using rotary encoders.
You could also use a servo pot to do this. It is analogue and you can count the number of times it goes over the top. However, they are quite expensive.