You can also use a classic-style wireless controller like 8Bitdo's SN30. You can use the NES Classic and SNES Classic Editions and their old-school controllers with more modern connectors, but they're still wired. Of course, they're also wired controllers that require an adapter if you want to use them with any modern system. The rectangle of the NES and the dog bone of the SNES controllers are simple, functional, and incredibly sturdy. Game controllers have come a long way since the 8-bit era, but there's still something satisfying about the classic gamepads of the early '90s.
Limited controls compared with modern gamepads.