The easiest way to win an argument is of course to be right, well done, full points to TheLady for that one. But it must be said that in real life, one would never rationally into an argument if one believed that they were wrong would they? Unless they have some evil agenda, but that is for the conspiracy nodes. In lieu of being able to prove that you are right there are certain ways of winning the argument, or at least converting your almost certain defeat into a draw.

1. Modulate your voice to fall out of sync with theirs.
Most people shout when others shout, whisper when others whisper, and try to match the other person's voice patterns to 'get on their level'. This rarely works in arguments, and they end up being shouting matches. So by making random changes to pitch, speed, cadence, and tone, one will find the other person begins to falter.

2. Look away, and be silent for a while in the middle of one of their tirades, and look back when you know they are about to finish, and when they stop to hear your response, say something like: "I wish things were different, I don't want to argue with you, I (like/love/adore/admire/hate) you, but if we have to talk this through can we wait a while so that both of us are calmer and more our usual selves. I need time to think hard about some of what you've said anyway."

3. Note the language,
if it is closed and non-varying, a good bet is that they are locked into one emotional level, and a way to win is simply to hug them. The flush of positive emotion this causes will destabilise them so look out for hits or pushes, but in the silence and their confusion you can deliver a new point assured that they will hear you.

4. Complement them in the middle of everything on something you know is important to them.
When they try to get back to the argument, tell them they don't talk about themselves enough, and that perhaps if you understood them better you would agree more with what they said. This one is pure genius and works 99% of the time.

5. If all else fails say this : "I refuse to have a battle of wits with someone who is unarmed. Goodbye."
Then walk away in triumph.

6. If even that fails and it is your girlfriend and the two of your are argued to near exhaustion, kiss her. Its probably what she wants right now.

Else run.