Nope, I don’t want you to help me break the law, but I thought that title might get me some quick attention! 
My actual query is a bit less mundane, but no less interesting, I hope.
I have often heard it said when someone is making a fantastical claim that if it cannot be falsified, it has no merit. Could any of you helpful Doper’s provide an example that would help illustrate this?
Russell’s teapot is the historical standard example in this regard.
Roughly speaking, falsifiability is necessary in order to successively approach a true description of reality; each falsification leads to your theories about reality becoming less bad, eventually converging on truth. A hypothesis that does not allow falsification precludes this development, it cannot be further refined, and thus can only be accepted on a basis of faith; hence, it’s generally judged unscientific.
Simply - to falsify claim X is to be able to say what the world would look like if claim X were not true.
Claim: There is a tree in front of you.
Falsification: There is no tree in front of you.
An unfalsifiable claim is not necessarily one that is true, but one that could never, even theoretically, be shown not to be true.
So, if I make the claim that an invisible, silent, substance-less being lives in this tree, there’s no way for you to ever prove me wrong. “I can’t see it,” you say. “Of course you can’t. It’s invisible,” I respond. My claim very possibly could be the truth, but there is no way to verify it one way or the other.
Another, more controversial example. Many people would say that Freud’s theories regarding the unconscious are unfalsifiable. “When you were young, you had sexual feelings regarding your opposite-sex parent,” he says. “But I don’t remember them,” you say. “Of course you don’t,” he says. “That’s the nature of your unconscious mind.” “Well, Mr. Freud,” you could reply. “How could you or I tell if I indeed didn’t have these feelings?”
Wow. Never heard of that before. Awesome.
Strangely, the image in the article is of Newell’s teapot, not Russell’s teapot.
Two more modern examples are the Invisible Pink Unicorn and the Flying Spaghetti Monster. They might be more well known now, but the teapot is a classic.