Burden of Proof
The Fallacy
Saying that the burden of proof lies not with the person making the claim, but with someone else to disprove.
Why it's wrong
The burden of proof lies with someone who is making a claim, and is not upon anyone else to disprove. The inability, or disinclination, to disprove a claim does not render that claim valid, nor give it any credence whatsoever.
Example
Bertrand declares that a teapot is, at this very moment, in orbit around the Sun between the Earth and Mars, and that because no one can prove him wrong his claim is therefore a valid one.