[simias]

The original GameBoy had a hardware LFSR that could be used to generate white-noise-like sounds. It was often used for "whooshing" effects and also cymbal sounds, such as in the famous Super Mario Land theme: https://www.youtube.com/watch?v=Gb33Qnbw520

[WillKirkby]

For more technical details on the exact LFSR used, there's this: http://belogic.com/gba/channel4.shtml

[khedoros1]

Ditto with the NES. It actually had two possible tap configurations with different sequence lengths, so that they have slightly different sounds to them.