Use headphones and start quiet — several of these depend on stereo separation and can surprise you.
A pitch that seems to rise (or fall) forever. Octave-spaced tones glide together under a fixed loudness window, so new tones fade in at the bottom exactly as old ones fade out at the top — the ear never catches the seam.
Play only the upper harmonics (2f–6f) of a tone and you still hear its pitch at the absent fundamental f — your auditory system infers it from the harmonic spacing. Toggle the fundamental in and out: the pitch doesn't change, only the timbre.
Headphones required for binaural. Two close frequencies, one in each ear, produce a beating you hear even though neither ear gets an amplitude fluctuation — the illusion is built in the brainstem. Switch to monaural to hear the real acoustic beating for comparison.
Two Shepard tones a tritone apart. Because their spectra are octave-symmetric, whether the pair sounds like it goes up or down is genuinely ambiguous — and different listeners hear it differently, apparently shaped by the pitch range of the speech you grew up with (Deutsch).
The tempo version of the Shepard tone — a pulse that seems to accelerate (or slow) forever. Layers of clicks an octave apart in tempo fade in at the slow end as the fast ones fade out at the top, so the beat never actually arrives anywhere.
Headphones required. A high and a low tone an octave apart swap ears back and forth. Most people hear a single tone bouncing between the ears whose pitch flips too — which is not what's actually playing (Deutsch, 1974).
Headphones required. A major scale is played ascending and descending at once, with each successive note alternating ears. Your brain regroups it into a smooth scale in each ear — reassembling by pitch proximity rather than by which ear actually received each note.