There are a bunch of interesting audio illusions that people can try. A couple of the main ones are binaural beats and the shepard tone.
Binaural beats have a few uses including therapy, although they can also be harmful and cause fits in people who suffer from epilepsy apparently. Two tones are played that are close in frequency to each other, with one in each ear. These combine in our heads to create a different tone.
The Shepard Tone gives an illusion of an infinitely decreasing or increasing pitch. It has been used in a few sound design elements over the years, including in the music for the endless staircase in Super Mario 64, and the Batpod in The Dark Knight films.
Check out samples of these and more at: