The video game emulator Delta lets one play NES, SNES, N64, Game Boy, GBA, and Nintendo DS ROMs (which are easy enough to find online) on your iOS device. The newest version now supports iPadOS features such as full screen and runs multiple games at once. Thanks to airplay, the games can be streamed straight to your AppleTV or other supported device.
Trying to play old Nintendo titles with touch screen controls proved less than ideal but after I hooked up a bluetooth Xbox controller, I found the experience to be like I remembered. It gave me quite the dose of nostalgia. I still died on that very first Goomba in Super Mario Bros, though.