1. Don't lose your cool.
If you lose your temper, you have lowered yourself to their level and are playing their game. They are trying to piss you off. Don't let them succeed. Maintain your composure and watch them explode with profanities and irrational arguments. They will be the ones that look stupid, not you.
2. Be ready to respond with something more clever than them.
If someone insults you or makes a threat, be ready to respond off the cuff. I'll give you an example. I currently have a day job as a telemarketer. One guy I talked to called me every name in the book. Then he threatened me with "I'm recording this conversation". I said "Good! You should sell the tape to a record company and make some money. I'm sure you'd be great entertainment for listeners. It wouldn't go well on radio though because they'd have to bleep out everything you say." He then cursed at me one last time and hung up.
3. Deliver your knock out blow.
If someone persists on threatening and harassing you, don't threaten them back. Simply act. This will throw your opponent totally off guard. I'll give you an example of this; I was harassed by a collection agency recently. They made illegal threats saying they would get a judgment against me and take my car and freeze my bank accounts. They also threatened me on voicemail. Unfortunately for them, they forgot to mention they were a collection agency, which is against the law. I promptly sent the voicemails to an attorney along with details of every conversation I had with them. My lawyer filed a lawsuit against them. A few months later the collection agency settled and I am $1000 richer.
Anyone who tries to dominate someone by fear is not a true leader. We need more people who rule without having to resort to scare tactics. I am ready to be a true leader. Are you?