Cartridge Adaptors will generally run most games on the SNES. The cartridge shape for the Pal SNES games and Super Famicom (The Japanese version of the SNES) is the same but the US cartridge shape is squarer and will not fit into a unmodified SNES without an adaptor in between the cart and console. Alternatively, you can file down the ends of the cartridge slot to make these games fit.
The Cartridge adaptors for the SNES usually have two slots on top - one is for your import game and another is for you to insert a cartridge from your own region. So if you wanted to play a japanese game, you'd put that in the front slot and then pop a Pal game in the slot behind it.
Success rates vary between Adaptors - and there is some trial and error unfortunately. For instance, the US wrestling game 'Hammerlock Wrestling' game refuses to load with newer adaptors like an Action Replay (the later games had protection to detect region differences between consoles) but if I use an old, simple adaptor with a UK cart it loads fine.