Poison, psychic, and flying all resist fighting attacks. Ghost is completely immune. Psychic and flying hit super effectively. The thing is though, fighting types are notorious in being able to 'cover their bases' and take out their counters. So watch out for stone edge, sucker punch, etc. In general you want to attack their special defense with special attacks, as traditionally fighting types have better physical defense- hitmontop/lee/chan being the exception.
