Zero crossing
The point where a waveform changes sign and passes through zero — the one place a cut is guaranteed not to pop.
Cut a waveform at the top of a peak and the level jumps from a large value to silence in a single sample, which the ear hears as a click. Cut where the wave is crossing zero anyway and the jump is next to nothing. That is why audio editors have a setting that snaps the selection to the nearest zero crossing, a habit inherited from cutting tape with a razor blade. With DC offset the trick breaks, since the wave may never cross zero at all.
How often it happens is a measurement in its own right. Zero-crossing rate is one of the cheapest features in audio analysis: voiced vowels cross rarely, hissing consonants and noise cross constantly. It was an early way to tell speech from silence and still serves as a rough pitch estimate when an FFT is too expensive.