Build a standalone digital LCD voltmeter that measures voltages up to about 55V using a simple voltage divider.
Smoothly control a DC motor's speed via PWM, a transistor, and a potentiometer as a manual control interface.
Turn Arduino into an adjustable on/off timer set with a potentiometer, with a safety note for controlling mains-voltage loads.
Build a clap- or loud-sound-responsive lighting system using an LM393-based sound sensor.