I quite like the idea of making an Arduino generate DTMF (Dual Tone Multi-Frequency) signals, and hence dialling numbers. Some years ago, you could buy small boxes with a keypad and speaker that would do just that, for use with pulse-dialling phones on lines that would accept DTMF.
It might also be fun to generate Quindar tones, as used by NASA in the Sixties to control the radio gear that they used on the Apollo missions: