My thoughts on the matter:
*The basic elements that make up life are some of the most common elements in the Universe. CHON (Carbon, Hydrogen, Oxygen, Nitrogen), all the main components of life as we know it, and perhaps Sulfur and Phosphorus which are vital to the functions of Earthly life.
* Water, also necessary to all terrestrial life, is one of the most common compounds in the Universe.
*We know that certain complex carbon and CHON compounds form naturally under a wide variety of conditions, including in deep space; many of these molecules, found everywhere from certain meteors and comets to distant nebulas and the clouds of gas around newly formed stars, are regarded as the "precursors of life", in that they form the basis for many of the molecular strutures common in living things.
* Despite having only limited ability to observe extrasolar planets for only the last few years, we have already found hundreds of worlds, including several that sit in the so-called "Goldilocks zone" (not too hot, not too cold) where liquid water might exist on their surfaces-- not to mention the possibility of nonsurface water, like that found inside the ice moons Europa and Enceladus right here in our own solar system.
* Life here on Earth, according to fossil records, began almost as soon as it was physically possible, shortly after the crust cooled enough for water to condense on the surface. Therefore we know that it is possible for life to form relatively quickly under certain conditions.
* The laws of physics that allowed such complex self-replicating structures to arise on Earth are, to the best of our knowledge, the same throughout the known Universe.
For those reasons, I think that life is most likely relatively common in not only our Galaxy, but most Galaxies. Of course, when dealing with something the size of the Galaxy, let alone trillions of them, "common" is a very relative term. If only one in ten thousand exoplanets has life, that's still hundreds of millions of worlds in the Milky Way alone.
As for intelligence, presumably meaning in this case a human-level capacity for abstract thought and creativity, well, life on Earth managed without us for billions of years, so we know it's not a necessity. The random nature of evolution means that there's no guarantee that a particular world will develop creatures whose brains work anything like ours. So I think that intelligence as we define it may be quite rare. On the other hand, as I said, the Universe is huge and there's plenty of room for trial-and-error variations to produce something that we might recognize as thinking beings. So it would not surprise me if somewhere out there some alien is wondering if we exist.
I'm a cynical optimist. I think the only way out is through, but once we get through it'll be better. Very different, but better. Howard Tayler
It is not the strongest of the species that survive, nor the most intelligent, but the one most responsive to change. Charles Darwin
"It is the duty of the writers to seduce me into suspending my disbelief!" Paul Beardsley
Power, Lord Acton says, corrupts. Not always. What power always does is reveal. Robert A. Caro