The Fermi Paradox is this; if life is capable of existing on a planet, and space travel is possible, then why have we seen no evidence of extraterrestrial life?
We know that life exists on one planet, so it is logical to assume that life exists on other planets. Furthermore, we know that intelligent life exists on that planet, so it is logical to assume that intelligent life exists on other planets. We know that at least one species of intelligent life has created space travel, so it is logical to assume that there are others. Even without space travel, we know that at least one species of intelligent life emits an enormous amount of radio waves from their planet, and broadcasts messages meant to find other like species. So where are these others? Why are we alone? There are a couple of solutions to this question.
The first, and most obvious solution, is that we're simply overestimating the ability of life to form. Yes, there are more than 100 billion galaxies, and yes, they each have between 10 million and 1 trillion stars. Yes, planets appear to be pretty common. And yes, life on Earth has been around for not all that long compared to the age of the Universe (3.5 million : 13.6 billion). But it just might be that intelligent life is such a rarity that we are the only example of it in the history of the Universe. In a less extreme example, it might be that life is so rare that none of it developed near us, or that we are a statistical fluke such that no evidence is visible from our viewpoint, or any of a hundred other variable might be shifted just so as to give the appearance that we are alone. This seems improbable, but when working from incomplete information all possibilities must be considered. Perhaps we were created by some hyper-intelligent being, who didn't deem it necessary to populate the rest of reality.
The Fermi paradox worries me, because of what it says about the survival of an intelligent species. On the existence of life on planets, we have one data point - Earth. On the existence of intelligent life, we have one data point - humans. On the existence of space colonizing species, we have no examples. Yes, it is theoretically possible, even probable. But without actually doing it, we can't say for sure that it can be done. I obviously have an appreciation for extrapolated trends, but if it's possible, why hasn't it been done? Why have we seen no evidence of our intelligent brethren expanding across the galaxy?
There's also the anthropic principle to deal with, which says that we wouldn't be here observing our loneliness if we weren't both here and alone. This does not satisfy me.