Yes, they can.
Higan is a really good emulator for NES and SNES. It’s in the repos of most distros.
Mupen64plus is a good N64 emulator - again, it should be in the repos of most distros. It’s a little glitchy sometimes, with certain games. But on the whole, most games are playable.
There are also emulators available for the DS, GameCube and Wii, but I’ve never tried them.
I think higan can run DS games too.