These images are included as references for Episode #0059 of our podcast.

Super Nintendo / Super Famicom
In order to play Super Famicom games on the Super Nintendo, you have a couple of options. As you can see, SNES games have grooves at the back/bottom of the cartridge, which lets it fit around the two tabs inside the cartridge slot of the SNES. The back of SFC games are completely flat. Knowing this, you can either (a) rip the tabs out of your SNES, or (b) groove some grooves in the back of the SFC cartridges, themselves (like our Super Butôden game has). The one-time route is definitely ripping out those tabs; all you need are some needle-nose pliers. For good measure, we also show one of the JP GameBoy games running on the SNES via a Super GameBoy; no mods required.
Sega Genesis / Megadrive
Similar to SNES/SFC games, the bottoms of Genesis and Megadrive cartridges are slightly different. The easiest route is definitely just getting your hands on a Genesis Game Genie, which has no physical restrictions at the top. Plug the Megadrive game into the Game Genie, plug the Game Genie into your Genesis, and you're good to go. 32X completely optional. It just looks funny.
Nintendo GameBoy(s)
From the original toaster GameBoy all the way up through the GameBoy Advance (SP), absolutely nothing extra is required to play a game from the same or prior-generation on that system. Plug it in and go. Batteries help.
Sega Saturn
For the Sega Saturn, your best option is getting a hold of a combined Action Replay / RAM cart. For us, we like the Action Replay 4M Auto Plus; cheats, extra RAM, game save storage, and import gaming goodness are abound. Make sure the Action Replay is plugged into the cartridge slot, throw in your Japanese game, and just select "Start Game" from the menu. Off you go into Shin Butôden land.
Sony PlayStation
You could have gone the mod-chip route, but game publishers started getting smart down the road and wouldn't let even non-bootleg games run if they detected a mod-chip. Of course, stealth chips came soon after... but who really wants to play a game of cat-and-mouse? The Action Replay devices that plugged into the original model's parallel port in the back were certainly the way to go. Tape worked in holding down the cover-button, but a perfectly-sized spring was certainly well-loved. Start it up with an American game, go to the file explorer, exit out, swap out the games, and start it up... Legends is on.