Aside from reading analog sensors, you can do a number of other swell things like monitor voltage, current and capacitance. I'm not going to go over them here, but you can read more about them on this page.
Step 1: Go get stuff
A resistor (220 ohm to 1K)
A capacitor (0.1uF)*
A potentiometer (or any other resistive sensor)
Wire and whatnot
*note that changing the capacitor will change the resolution of the circuit. To increase the resolution, you simply need to increase the size of the capacitor. Try using a 1uF electrolytic capacitor and compare the difference (remember that is is polarized and the + side should connect to the power source).
The resolution can also be changed, but less significantly, by changing the resistor value. Just make sure to keep it in the range of 220 ohm to 1K.
Step 2: Build the circuit
Using the breadboard connect the other end of the 1K resistor to one of the legs of the capacitor and one of the outer pins of the potentiometer.
Connect the middle pin of the potentiometer to ground.
Connect the other pin of the capacitor to +5V.