If they are fighting bloodlines ( siamese fighters) then nothing.
However bettas ( show and pet stock) it depends on the fish in question and the tank setup. I have kept rasboras with them, but they are so active, it stresses the betta. Glo light tetras, head and tail lights and neons are good, they school and usually stay away from the betta. Mollies/ platys will get nippy with the finnage, Corydoras do ok, bristlenose plecos do ok. But again it depends on the size of the tank and the betta.