Any discussions of the size of the universe will lead to the Fermi Paradox: given the enormous numbers of stars and the billions of years of existence of the universe, it seems obvious that life must have evolved zillions of times, and advanced space-faring civilizations can't be too uncommon. So where are they?
Consider our own Milky Way galaxy, with roughly a trillion stars. If only one out of a thousand stars has planets that develop life as we know it (as happened to the Earth quite early, some 4 billion years ago), and only one out of a thousand of those managed to develop complex life (as began on Earth about 500 million years ago), and only one out of a thousand of those developed intelligent life with a technological civilization, then there should still be a thousand such civilizations in the Milky Way. Where are they?
Also note that our sun is relatively young at 4.6 billion years. The oldest stars in the Milky Way are some 13 billion years old. Time for a little digression.
Man is an aggressive species. That may well be the case for all technological civilizations, as the humble are likely to huddle and die instead of expand and thrive. If we assume that mankind successfully moves into space (such as our own asteroid belt and cometary halo--see Our homes, the Comets), it is likely--nay, inevitable--that mankind will slowly advance into the cosmos in spite of the speed of light. It may take hundreds of years for a self-sufficient mobile comet to travel from our sun's environment to another star, but there they will find more comets. Room to grow, resources to thrive.
If we assume that only one interstellar colony is founded every hundred years by the inhabitants of Sol's Oort cloud, and then after a hiatus of a thousand years, each of the new star systems begins it own replication, slowly, one colony every hundred years, then humanity will still sweep over the entire galaxy, occupying the cometary halos of all of the stars in the Milky Way in only five or ten million years.
This is a tiny span of time in geologic terms, and a blink of the eye in the life of the universe. How could it not have happened, thousands of times already? That is the essence of the Fermi Paradox.
We see zero evidence of other life, let alone technological civilizations, present or past. The SETI (Search for Extra-Terrestrial Intelligence) project has searched the skies since 1960 with zero tangible results. We have found zero evidence that alien intelligences have visited the Earth in the past, and of course no evidence that they are here now.
Are there alternative explanations? Of course. Perhaps they wish to stay hidden (a non-interference doctrine). Perhaps their technology is so advanced that we can't recognize it, or simply works in a way we aren't looking for. Perhaps the scale of their lifespeed or technology is such that we can't recognize it (nanobots, or perhaps they only appear for a millisecond every millenia). Perhaps they are from an ocean world and we should be looking miles beneath the surface where they maintain a lab. Water worlds should be much more common than Earth-like worlds--see Earthlike Planets.
And perhaps they are computers, not terribly interested in mere, slow, organic life, and their presence will be obvious once we speed up our perceptions and intelligence by a few orders of magnitude.
In some ways, the alternatives are frightening. The odds of us being the first technological civilization in the galaxy seem remote. That leaves the likelihood that life is precious and rare, or that the universe is a very dangerous place and we will soon succumb to the odds. Supernova, gamma-ray bursters, enormous black holes in every galaxy spewing deadly torrents of radiation, supervolcanoes, solar flares, not to mention planet-busting asteriods, all pose threats to civilization and life itself.
Or still worse, there is a chance that intelligence is the opposite of a survival characteristic. Perhaps we are dooming ourselves by squandering our resources, changing the ecology of the planet, or will effect the same result by blowing ourselves up. Perhaps every time intelligence appears, some idiot invents a super-bug which destroys all life, or creates advanced computers which eliminate all competing intelligent life. Or perhaps there is some simple experiment that every intelligent species eventually tries that destroys their home planet.
It may only be a matter of time.