The Bad Buffalo (simply Buffalo in Mother) are enemies in EarthBound Beginnings and EarthBound. In the first game, they only appear as very tough enemies around Ellay. Though it has high defense and attack, it can be defeated easily by PSI abilities. They can appear in groups of two and three, and will often get smash attacks. It rewards a decent amount of EXP and money when it is defeated.
In the Wii U Virtual Console release of EarthBound, if everyone in Ness' party dies except for Ness, and Ness fights it, there is a glitch where the Bad Buffalo will waste a turn by "Knitting its brow" which is something only the Violent Roaches do.