Building relationships with the other person. You understand better what they want and where they want to go, and you can discover some more. Negotiation does not have to viewed as a way of destroying or stressing out relationships.
You can build trust and demonstrate trustworthiness. If there's a disparity in power, leverage, information, AND you're dealing with a party what's gonna use that and take advantage you can leave the room feeling abused.
Having a good day, because you negotiated. Some days of negotiating you look forward to and are the best days. Others you dread.
Getting a good deal. Negotiating as a success means getting what you want for a price that's acceptable to you.
Become a trusted negotiator. Who has high character, competent, and empowered to make a decision. That is the right party for the other person to deal with.
Figure out the BATNA - best alternative to negotiation agreeing.
Get something out of it. If someone's shouting and threatening, you can get the high moral ground or at least information.
Inside negotiations are the toughest. They're the least forgiving. And the most important ones to lose.
You can get to a deeper level, when you know you're not going to agree. You can sit down with him and say OK here's where I think our conflict is coming. 'What would it take to develop a better relationship? What would it take to make this deal?'
Create a lasting agreement with some elasticity down the road, that doesn't terminate in a lawsuit six months later. A function of how how much trust you've developed.