My two daughters fight a LOT, but they also love each other, kiss and hug. They have learned to say, "I forgive you, please forgive me" every time one has offended the other. Often I will both of them do that to each other. They can also say, "God forgives, I forgive". When it's been REALLY bad, i have them bow to each other and say, "Forgive me, I forgive you!". Obviously there has to be some forgiveness in between the fighting. I WOULD intervene for the simple reason that my youngest is smaller than the oldest, and the oldest tends to push her weight around. Sometimes I'll stop everything and give both of them a hug at the same time, and try to be calm and give everyone a sense of peace. If you believe in God, you can also tell them, God is very sad when people fight. He wants you to get along, I want you to get along. Read peaceful books, and make sure you have a peaceful attitude in the house.
Also, I make sure the TV influence and movies is at a MINIMUM. They are little sponges, and soak that up like nothing else. Even the childrens' movies are often inappropriate for children. Whatever happended to respect and manners? Sexual innuendoes in childrens' movies? If you've seen Alvin and the Chipmunks, you know what I'm talking about. Not to mention rudness to parents, disrespectful to each other. I was VERY sorry i brought my children there - they immediately accted up for 2 days. The movies are getting worse every day.
Separate them in separate rooms whenever they start to fight. They can have a time-out seat, just like in "The Nanny". I have put rules on the wall, that include being polite, respecting one another, clean room, etc. and they get stickers when they comply. I also give them rewards such as MacDonalds if they get along for a week. If they start to fight I remind them - do you want to go to Mickie D?
If they fight, they are also not allowed to be with friends (birthday parties get cancelled) TV, or movies. Sometimes there is a behavioural issue that needs to be addressed in one child that is causing issues. My older daughter tends to be a little arrogant and also overbearing. So I'm also working on teaching her to be more gentle and let others have opinions as well. It's a slow process, but it's progress.
God bless.