Yamaha was responsible for them. The earliest game to use one was Marble Madness arcade by Atari in December 1984, which used a YM2151 soundchip in stereo mode and was used in perhaps most arcades and Sharp X1 and X68000 desktops, some with other soundchips including OKI M6295, Konami K007232, Namco C140, SegaPCM and NMK112. My favorite is either the YM2151 or YM2610/YM2610B. YM2151 is a classic, while YM2610/YM2610B is like borderline between beeping and realistic quality instruments.
Can't go wrong with the YM2612. It has a bum rap due to so many sound designers back then being lazy and settling with just using the presets in the GEMS engine, which itself was capable of pretty good stuff (Earthworm Jim for example).
I would have to go with the YM2151, as it is featured in so many fantastic arcade games. Second to that I would pick the Saturn's SCSP, a true FM/PCM monster, often underappreciated...