Argumentum ad ignorantiam
Argumentum ad ignorantiam means "argument from ignorance." The fallacy occurs when it's argued that something must be true, simply because it hasn't been proved false. Or, equivalently, when it is argued that something must be false because it hasn't been proved true.
(Note that this isn't the same as assuming something is false until it has been proved true. In law, for example, you're generally assumed innocent until proven guilty.)
Here are a couple of examples:
"Of course the Bible is true. Nobody can prove otherwise."
"Of course telepathy and other psychic phenomena do not exist. Nobody has shown any proof that they are real."
In scientific investigation, if it is known that an event would produce certain evidence of its having occurred, the absence of such evidence can validly be used to infer that the event didn't occur. It does not prove it with certainty, however.
"A flood as described in the Bible would require an enormous volume of water to be present on the earth. The earth doesn't have a tenth as much water, even if we count that which is frozen into ice at the poles. Therefore no such flood occurred."
It is, of course, possible that some unknown process occurred to remove the water. Good science would then demand a plausible testable theory to explain how it vanished.
Of course, the history of science is full of logically valid bad predictions. In 1893, the Royal Academy of Science were convinced by Sir Robert Ball that communication with the planet Mars was a physical impossibility, because it would require a flag as large as Ireland, which it would be impossible to wave. [Fortean Times Number 82.]
See also Shifting the Burden of Proof.