A absence of evidence is often cited in the debate regarding the existence of other life in the universe. We have never received signals from ET and, while there have been tantalizing hints of life on Mars, nothing has even come close to being confirmed. So with no evidence, are we forced to just admit that we are the only lifeforms in the universe? No, we have just begun to scratch the surface of looking for life beyond the Earth. Just because we don't have evidence yet doesn't mean we won't find it.
This idea can be taken too far. Just as we have a absence of evidence for life on other worlds, we also have a absence of evidence for unicorns. It is logically impossible to prove a negative (like unicorns don't exist) so are we forced to accept them as equal possibilites? In science, we can assess the plausibility of a claim. It is highly plausible that there is life outside the Earth that we have yet to find considering how little of the universe we have explored. We have however, explored a vast majority of the land mass of the Earth and have yet to find unicorns. While there is nothing intrinsically impossible about a horse evolving a horn, we just haven't found it in our explorations. So, while a absence of evidence may not be evidence of absence, we can still use current knowledge to judge the likelihood of different claims.
The other way people try to use the gaps in our knowledge is to prove claims. This is known as the argument from ignorance. In my experience, this is one of the most common logical fallacies. The basic argument goes because we don't understand X, Y is true. This is often invoked with quantum mechanics. People will make arguments to the effect that because we don't understand the quantum world, psychics really have powers. The same argument could have been used only a few centuries ago to say because we don't understand flight, humans can fly by flapping their arms. You can't use our lack of understanding to prove anything.
It is not hard to find people on the internet and in real life committing both forms of this flawed logic. Whenever you encounter a claim, make sure you ask yourself if they are using unknowns to make their arguments. Are they asserting someone is true because we don't understand something? When it comes down to it, a lack of evidence is evidence for nothing.