Opening Disclaimer 1: Although there may be more than one universe, as per the hypothetical multiverse, we will humbly submit to our own bubble of information, the sphere with a radius equal to the distance light has traveled since the beginning of time some 13.8 billion years ago. Factoring in the expansion of the universe, this radius is about 46 billion light years.
Opening Disclaimer 2: By life, I mean any self-sustaining chemical reaction network capable of metabolizing energy from the environment and of reproduction following Darwinian natural selection. So, no spiritual machines way more advanced than we are or bizarre star-dwelling intelligent clouds or wormhole-inhabiting swarms of nanobots. Flying spaghetti monsters are fine.
OK, with these cleared out of the way, we can start. Perhaps the most striking result of modern science is that the same laws of physics and chemistry apply across the vastness of space and time. Think of it: we are now able to look at stars and baby galaxies billions of light years away from us. We find that they have the same chemical elements (albeit in different ratios) and that they evolve according to the same dynamic laws as our own sun does. The physical and chemical laws are the same everywhere and everywhen.
We also know, and this is another striking result from modern astronomy, that most stars come with a court of planets. And planets tend to have moons. Each one of these is its own world, with different physical properties and chemical makeup. There are large and small planets, rocky and gaseous, with many moons or with just a few or with none; planets may spin with a large or small tilt (the Earth's is 23.5 degrees from the vertical; Uranus's is an amazing 97.7 degrees), have thicker or thinner atmospheres with different gases in it, and so on.
In round numbers, and just in our own Milky Way galaxy, there should be about a trillion worlds, each and everyone a unique entity.
To these we add that there are hundreds of billions of other galaxies within our cosmic bubble and we come to some trillion trillion worlds in our universe, give or take a factor of 100. (A geeky comment: funny that this is so close to Avogadro's number, the number of atoms in one gram of hydrogen.)
At this point, you may say, well, within this staggering variety, pretty much everything is possible. Well, no!
The unity of the laws of physics and chemistry act as a very powerful constraint on what can and cannot exist. Even if in science — as long as the laws of physics are satisfied — we can't really rule out what can't exist, we can use the laws of physics and chemistry to infer what might. Point in case, the flying spaghetti monster is quite plausible, a cousin of the octopus that ventured out of the pond some billions of years ago on planet Mumba and, after some millions of years, grew feathers on its tentacles and took flight. Or, if not feathers, some ballooning mechanism with hot air from its digestive tract.
So, what can we expect to find as we scan the vast collection of worlds and search for living creatures? No one truly knows the answer to this question, although we can make educated guesses:
1. Life will be carbon-based. Why? Because carbon is the easy going atom, able to concoct all kinds of chemical bonds better than any other. A poor imitation is silicon; its biochemistry would be severely limited in comparison. And life needs versatility to thrive, that's its main prerogative.
2. Life needs liquid water. Yes, you can find frozen bacteria in the permafrost, but they aren't living. Since life is, in essence, a biochemical reactor, it needs a solvent, a medium where the reactions can unfold. Ammonia is sometimes proposed as a possibility. But it's a gas at room temperature and liquid only below -28 ˚F at a normal pressure. So, a cold planet with heavy atmosphere could have liquid ammonia; but that's pushing it. Water is this magic substance that is transparent, has no smell, no taste, expands as it freezes (a key property for water-based life in colder climates since there is liquid water below the ice), and is our own main ingredient.
Given these two constraints, the essence of life should be simple: carbon+water+other stuff (at a minimum nitrogen and hydrogen). The details, though, are not.
Each planet that may contain life will have its own history. And so, life there will have its own history, completely contingent on its hosting planet's history. This means that natural selection acts as a history-based pressure for survival, each tale a different one.
As a consequence, and despite its common carbon-water essence, there won't be identical life forms on different planets; or at least the odds will be extremely low. And the more complex the life form, the lower the odds that it will be replicated elsewhere.
If the flying spaghetti monster exists, it will exist only in one world. As we exist in only one world. We are the only humans in this universe. And if we consider what we have learned from the history of life on Earth, chances are that intelligent life is extremely rare. While intelligence is clearly an asset in the struggle for survival among different species (our fellow cavemen clubbed to death all the mastodons, didn't they?), it is not a purpose of evolution; evolution has not purpose, no final goal.
Until it becomes intelligent, life is happy just replicating; with intelligence, it will be unhappy just replicating.
Putting all this together, we realize that we are indeed connected to the rest of the cosmos chemically and that we share the same basis for life as any other hypothetical living thing out there. At the same time, we are unique, as are all other living creatures on this planet. Life is this amazing force that, from a carbon-based code and a common genetic ancestor, can create a staggering diversity of wonders in this, and possibly other, worlds.