@Morrus;The observable universe is of finite size. The observable universe is also of finite age, and thus finite size is the reasonable estimation of the size of the universe from known facts. It's possible that there exists an unobservable universe but anything outside our light cone might as well not be in this universe, so lets assume the universe is finite. We can estimate the number of atoms, galaxies, planets and so forth in the universe. We come up with very large numbers, so 10 to the 60th power or 80th power or whatever. The exact number doesn't matter for the next reason.
However, these seemingly large cosmological numbers for the breadth of time and space are trivial compared to the complexity of the information contained in the most primitive life forms we are aware of. Indeed, they are trivial compared to simplified DNA structures which we know are insufficient to support life. For example, the number of possible combinations of mitochondrial DNA in a typical vertebrate species is something on the scale of 10 to the 1000th power. Worse, the number of combinations that fold into any sort of protein, much less ones helpful for promoting homeostasis, energy consumption, and all the other things necessary for life to function is known to be very much smaller than the scale of possible combinations. Add to that the complexity of the surrounding hardware necessary to process that information, and it becomes incredibly unlikely that life will spontaneously generate from non-life. It is so incredibly unlikely that there is no reason to believe that it has happened more than once in the universe, and at the least there is no reason to believe that it has happened so often that any two planets in the universe support life at the same time. The frequency of spontaneous generation is probably so low, that it is lower than average life span of a living world before it gets wiped out by some cosmological catastrophe. Barring the discovery of some previously unknown self-organizing principle that causes life to appear at rates faster than random chance, we are almost certainly alone - the first technologically advanced species in the history of the universe. It's likely that not only is nothing else out there that can hear us, but that every other world is sterile.
There are various objections you can make to this line of argument, but they all prove to be very weak upon inspection. The most common to come up is to say that I'm only speaking of "life as we know it". But the more we know about how life works, and the more we realize life is actually nothing more than very complex machinery that processes information, the fewer alternative possibilities for arranging life exist. If you start looking at variant chemistries that might support life at other temperatures and pressures, they all turn out to have immense problems for sustaining life compared to the carbon/water based sort we do know about. It's not at all clear that any other sort of life can evolve in this universe, and if it could it's equally clear that the possibility of it evolving is even lower than the sort we do know about. Hence, "life as we know it" likely to be the only sort that exists.