The answer would really depend on what kind of fight you are talking about here. A brief explanation would have really helped in answering this question. However i would assum you are talking about general fights in public places and answer accordingly.
The answer is pretty simple, don't get into the fight if it's none of your business. You are eventually going to hurt yourself both physically and emotionally.
I just found the category is 'gender and relationships', so i would have to give another answer. So, here it goes...
Fights in a relationship do occur a lot of times. Give your partner some space and try to talk about the 'subject' which caused the fight. And if you are wrong then admit it or if you aren't, don't make a big fuss about all those small things in life.