If this galaxy is full of aliens, one of these mighty civilizations would already be old enough to be spread throughout the galaxy. They are all around us. How to we have not met before. Today this is known as Fermi paradox. To make this even a paradox, we must assume that the galaxy is full of developed civilizations. This is exactly what the SETI project is trying to prove.
To an ancient galactic civilizations won the whole galaxy needed very short time compared to the age of the galaxy, even if the wave of expansion moving at speeds much lower than the speed of light. It takes time in various models ranges from 5 to 100 million years for our galaxy. Although it seems like a long period, it is almost nothing compared to the age of the galaxy. Humanity already possesses the technology and ideas for such a journey - if we really care about we could begin to deal with colonization. Therefore, it is strange that we have not discovered any other civilization that already does this. The galaxy has a lot of older stars than our Sun and its planetary systems can live race much older than us, the race that had those 50 million years. So, why they are not here?
One possible explanation may be that they do not exist. It is possible that everything that happened on Earth seemed to start life on it, and this is too large set of random process to be repeated anywhere else in the universe, what makes us unique. The second and only remaining solution is that they are there, but we do not see them. If all the civilizations that reach our level of development, those that are able to emit radio waves, soon after be destroyed in some other way, not long enough to broadcast signals, and therefore we have less chance to detect them. Of course, this means that any advanced civilization awaits a fatal destiny, so this is true even for us.
Although it may be difficult to imagine that the end of our civilization is closer, there's an idea that proves just that. At issue is the Doomsday Argument, which is the most famous example of so-called anthropic principle, a specific philosophical school of thought that has received particular attention in the last years. The essence of all Anthropic ideas is the so-called Self-Sampling Assumption, the principle of reasoning by which each observer himself treated as a random sample of some groups. Word observer is drawn from the basic context and used for any random sample of anthropic reasoning.
Also, one of the possible options is a kind of global "conspiracies" of extraterrestrial civilizations. In fact, maybe all of them are hiding from us in all possible and impossible ways: they moved somewhere where we can not see them, communicate with each other only by some kind of electromagnetic radiation or they have already arrived in our solar system and watching us with a safe distance.