One of my favourite logical fallacies is the argument from ignorance or Ad ignorantiam. This is lucky as it is one that gets quite a workout in the paranormal and related UFO camps. The basic explanation of this fallacy is as follows: that the absence of knowledge is a positive argument for a position. In other words that a lack of information is itself proof. For example, those that favour the alien spacecraft explanation of UFO sightings may assert that as we cannot attribute every occurrence of lights in the sky to natural phenomenon, aircraft, weather balloons, swamp gas etc. this proves extraterrestrials are visiting Earth. In this way proponents can take negative evidence and turn it into a positive argument for the existence of aliens.
Another example is of hauntings, often these will consist of feelings, lights and sounds. If a rational reason for these is not readily apparent or cannot be found it is natural for some to leap to the conclusion that it is caused by ghosts. Hear a rhythmic banging at night? must be a ghost. Are there unidentified soft voices audible in your home? must be a ghost. This fallacy is a very easy trap to fall into due to our innate need to have a narrative that explains the world around us and does so in a way that conforms to our preconceptions about how we think the world should work.
The fallacy can also work the other way, by citing negative evidence as definitive proof that something does not or cannot exist. The difference with this side of the fallacy however is that continued negative evidence increases the strength of the argument whereas the reverse is true for the cases above. For example were I to say that I have not seen fairies at the bottom of my garden therefore they do not exist, this would be a fallacy. However, the experiment of people failing to see fairies happens millions of times a day and so makes the case ever stronger, but not certain. You never know.