This is my favorite tactic to employ when dealing with an argument that isn't an argument. Usually I whisper when someone decides to raise their voice and turn an informative conversation to an argument. In example, I might be discussing a news topic that is controversial. I will be explaining an article I happened upon, but the person hears the explanation as stating a personal opinion that s/he disagrees with. Instead of joining in on the yell-athon, I just speak very softly until s/he shuts up to hear what I'm saying. If it doesn't work, skip down the list to the end.
Example Argument: THAT'S JUST RIDICULOUS! WHO WOULD EAT BABIES TO SOLVE POVERTY! THAT'S DUMB! YOU'RE DUMB! (Useless argument because as stated above... some people don't listen well.)
Example Response: I was just talking about a satire Jonathan Swift wrote... you're illiterate.
Yell About Something Unrelated
I reserve this tactic for when I am arguing with a good friend. Once I realize that the argument is useless, I just start a new argument that is more entertaining/ridiculous. I don't segue; I just start in on it full steam. As for fair warning, the person talking at me usually doesn't like this at all. His/her reaction can be very encouraging.
Example Argument: The war in Iraq is necessary in order to show the terrorists what for, and to decrease the price of gas! (Useless argument because, I could care more about ferret farming than politics.)
Example Response: Chinchillas are the only acceptable pet rodent. Hamsters are the pets of peasants!
Agree With Them Completely
A strategy best applied when I realize there is no winning, and the argument is of no consequence. It's important to agree verbally. I would suggest an "absolutely" or a "you are completely right." Saying "uh-huh" or nodding does not do enough. It's also important to not agree ironically or sarcastically. It's also important not to elaborate. The point is to end the argument, because there is no argument. Elaborating might start up an argument where you are agreeing with each other... just loudly.
Example Argument: Don't go to art school, because you'll never make any money. (Useless argument because a. It's your life not his/hers and b. What the heck? Are you talking to a psychic?)
Example Response: You are absolutely right.
Take Their Argument Too Far
If agreeing doesn't quite shove them over the edge... agree and then blow his/her argument way out of proportion. This is the anti-argument tactic that utilizes faulty logic. Look at any example of slippery slope for ideas.
Example Argument: Don't go to art school, because you'll never make any money.
Example Response: That's right; I'll end up living in a cardboard box, painting poo murals and selling my organs to make ends meet! (Hopefully, they're just embarrassed, because they can't come up with anything worse. Even more possibly, they're just imagining possible themes for your poo murals.)
When in Doubt, Walk Out
Personally, I like to a get down and dirty and skip to this. I just walk away. No ands, ifs or buts about it. Just a person talking at someone walking away from his/her stupid, contorted face. Because no one looks good angry.
I would give an example, but I was too busy walking away from whatever was loud to listen to his/her topic.