How common is life in the universe? To answer that, we have to first answer the question: what is life?
What is life? Life is a complex self-organizing network process capable of reproducing itself. In other worse, it is a self-organizing system capable of self-reproduction -- creating another, very similar self-reproducing self-organizing system.
Self-organization is a feature of the universe itself. And as an environment at a particular level of complexity is filled, new levels of complexity emerge to create new environments to be filled. Atoms to molecules to chemical cycles to living things to social species to humans and their social environments. Re-run the universe, and you get life. And you get life over and over and over in a variety of places. And you get human-type intelligence as well, eventually.
Life is extremely common because self-organizing processes are extremely common. Life is simply a subcategory of self-organizing processes. It is simply a certain level of complexity of self-organizing processes. Given that, we must assume that life is common across the universe.
If we assume that the number of atoms in the universe is 10^80 and that life is exponentially more complex than is atomic complexity, and that therefore life is likely exponentially less common, we could come to some number of living things that would suggest how common life may be.
First, consider that the number of atoms that make up the earth is about 10^50. That should give you some idea of how big 10^80 truly is. It has been estimated that the number of living things that have existed on earth throughout history is about 10^40.
There are various estimates of the number of habitable planets in the Milky Way. I'll pick a low number simply so we can extrapolate it to all the other galaxies. So let's say there is only 10 billion = 10,000,000,000 = 10^10. If there are 100 billion galaxies, that means about 10^20 habitable planets in the known universe. Thus, number of living things on earth multiplied by number of habitable planets is 10^60 living things throughout the history of the universe. So life is common.
More, we only have to have life emerge once per planet. That's only 10^20 times that self-organizing self-reproducing systems had to emerge. Given that atoms had to emerge 10^80 times, this is a truly small number of times it had to emerge. It seems highly unlikely it didn't, over and over and over again.
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