Actually, I think it is best if we don’t, at least not as we are now. It would be a risk for ourselves as well as for all the other intelligent species there are in the universe. We have to change in some way before there is a decent chance of this having a “good outcome”. I think our priority should be firmly to protect and preserve Earth, Carl Sagan expressed a similar sentiment in Pale Blue Dot

"The Earth is the only world known, so far, to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment, the Earth is where we make our stand."

IS IT PRACTIALLY POSSIBLE

Practically, I think we could do it. There are many habitable planets out there. These are just the best ones we know of.

THIS IS NOT STAR TREK THOUGH

There’s a tendency to think it would be like Star Trek. But that’s a very idealized picture and even then you have the likes of the Borg in their universe. What happens a million years into their future? What happens to the various large scale conflicts that have already happened just a few thousand years into that new era of space faring civilizations? Even the rather idealist Star Trek universe has many seeds for potentially endless chaos a few thousand or million years down the road.

But Star Trek is just the products of talented script writers’ imagination, not future casting. Makes lots of implausible assumptions. For instance that ETs throughout our galaxy have similar exobiology and often even compatible DNA, can all eat each other’s food nearly always, and that they are all basically humanoid, and usually looking more like each other even than humans look like gorillas, never mind elephants or parrots or octopuses. And all arose independently around multiple star systems at the exact same moment of time to within a few thousand years. They have an “in house” explanation based on the ancient humanoids who billions of years ago seeded worlds throughout the galaxy and who were so advanced they could arrange for them all to evolve humanoids at the exact same moment more or less, billions of years into the future. And borders between stars light years apart that are measured and patrolled exactly to the kilometer. It’s fun but requires a lot of suspension of disbelief if you are scientifically minded.

WHAT WOULD HAPPEN IN OUR REAL UNIVERSE?

Instead, imagine a galaxy filled with peaceful colonists, yes, maybe some pirates etc as in Star Trek - all originating from Earth (vastly improbable that they arise simultanously on multiple worlds like Star Trek at the same time).

Then amongst them, here and there, you have the likes of ISIS, North Korea, Hitler, whatever present or past figures you imagine as the worst we could have - they would all be in space in the colonies, people like that. But now give them the technology we would have several centuries into the future. They have the ability to make self replicating machines probably, and cyborgs, and uplifted animals of all sorts made intelligent by DNA manipulation.

Now let them expand through the galaxy - so that they are beyond reach. Assuming we don’t get warp drive, which is very sci. fi. at present - then if some of our descendants are a thousand light years away, which is only a hundredth of the diameter of our galaxy, we wouldn’t even know what they have done more recently than a thousand years ago.

EXPANSION OF A SOCIALLY PRIMITIVE, TECHNOLOGICALLY ADVANCED CIVILIZATION THROUGHOUT A GALAXY

We are technologically advanced, yes, at least compared with previous generations here on Earth,but that example shows that socially we have a lot of catching up to do to be ready to use this technology on a galaxy spanning scale. I can’t see any way that such a galaxy could be anything but total chaos. This expansion of technological civilization into a galaxy would also quickly go exponential, and favour the most aggreessive and most rapidly reproducing species.

The most aggressive colonists wouldn’t need to set up stable civilizations even, as they would probably have the ability to live in the Oort clouds, with fusion power. In that future, maybe just a few centuries ahead, small groups, even just family groupings or a few friends on a whim, could just hop from one comet to another throughout the galaxy as those clouds of comets mingle and probably spread most of the way to the nearest stars, probably all the way to nearby Oort clouds around other stars.

FILL GALAXY AND THEN UNIVERSE

They could then fill our galaxy in the not so distant future. A long time perhaps in human lifetimes, but compared to geological time, just a blink of time. Probably in less than a million years. Crossing over to other galaxies is quite a challenge - but the space between galaxies is not devoid of material. There are stars in between and gas clouds also, and with the technology we’d have by then we’d probably be able to move planets with fusion suns, at close to the speed of light, a bit like the Puppeteers in the Larry Niven novels. There are parts of the universe disappearing beyond the speed of light horizon under its expansion, so without warp drive it would be limited, but we could spread to millions of light years, eventually billions of light years in every direction. If we set it off here, without foresight and planning, that’s surely the inevitable outcome.

So - in principle, yes we could fill the galaxy and much of the universe also, at least of the part closest to us.

But, if we did it as we are now we wouldn’t turn into a galaxy and universe spanning civilization.

We’d become a galaxy and universe spanning chaos of beserker robots and creatures just running amok. Not our selves necessarily.

NIGHTMARE FUTURE

I think a future like that would be the worst nightmare not just for us but for any beings in this galaxy and eventually universe. If someone somewhere establishes a peaceful spot in the galaxy - they would never know when some horde of beings with strange ideas would suddenly appear having developed for a thousand years over a thousand light years away - and then arrive at close to the speed of light using unfamiliar technology. They would be our distant cousins, or the creations of our cousins, but that wouldn’t help. And once started, how can this ever stop?

Even if people learn to co-operate in one part of the universe - that’s only going to work in a small region, perhaps a few tens of light years in diameter. Beyond that, the chaos would just start up again or rather just continue without check.

Also you just can’t keep expanding exponentially. At some point you have to stop. So why not stop at a point where you have some reasonable control and reasonable prospects for your civilization for the future?

SO NO SENSIBLE ET WOULD BE A GALACTIC IMPERIALIST

For these reasons I think that no sensible ET would set out to colonize a galaxy. Not in an emperialist conquering way at least. If they do explore the entire galaxy it will be in some way that involves restraint and has minimal impact on the galaxy, chances are.

There’s plenty of space. We could have countless trillions of us in a single star system. There’s enough material in just the asteroid belt of our solar system for a thousand times the land area of Earth - so that is already a population of trillions living in comfort if we develop that technology.

SETTING UP NEW COLONIES BEYOND THE HORIZON OF COMMUNICATION WITHOUT FORESIGHT - LIKE A NUCLEAR BOMB IN YOUR HOME CITY

So, I expect our galaxy to quite possibly have trillions of colonists from various ETIs, but they would keep them localized in a small region. Setting up new colonies “beyond the horizon” of your civilization without foresight about the possible effects would be seen like letting off a nuclear bomb in the middle of your home city. Something that no sane person, or being, would do.

I think they, and we also, should use robots instead. That is something we can do safely, carefully designed robots. We don’t need to give them the ability to evolve at all. Perhaps replicating only. And limit the number of replications and there are many other things we could do to keep them safe.

WE CAN BE ONE OF THE WISE ETS

I think, there is evidence that we may be wiser than the most reckless ETs possible, which might destroy themselves in space wars pretty much as soon as they begin on spaceflight. Carl Sagan refers to this as "the intrinsic instability of societies devoted to an aggressive galactic imperialism".

Though we have stumbled a lot, we have made many good decisions, such as dealing with the problems of DDT and CFCs, human rights (a lot of progress though much still to do), preventing chemical and biological warfare (even in the almost all out conflicts of WWII neither side used the chemical weapons of WWI, I know there have been exceptions but most wars don’t use them).

We've developed nuclear weapons, and yet, for decades we haven't used them. Indeed Carl Sagan suggests that maybe nuclear weapons are the deciding factor here. After talking about our own efforts to deal with nuclear bombs he then goes on:

"If every civilization that invents weapons of mass destruction must deal with comparable problems, then we have an additional principleof universal applicability. Weapons of mass destruction force upon every emerging society a behavioural discontinuity: if they are not aggressive they probably would not have developed such weapons; if they do not quickly learn how to control that aggression they rapidly self destruct. Those civilizations devoted to territoriality and aggrssion and violent settlement of disputes do not long survive after the development of apocalyptic weapons. Long before they are able to make any significant colonization of the Milky Way, they are gone from the galactic stage. Civilizations that do not self-destruct are pre-adapted to live with other groups in mutual respect."

He goes on to say that because we have only just reached this stage then this future scenario of mutual respect may seem unlikely because of our short term perspective, and that the required changes may take a thousand years or more for us to reach maturity as a species. From Carl Sagan's "The Solipsit approach to Extraterrestrial Intelligence", 1983 .

We’ve prevented starvation with the often forgotten Green Revolution between the 1930s and the 1960s, stopped nearly all whale hunting, lots of work to preserve species and environments etc.

If you compare our present world with what it could have been without all those initiatives - I think it gives room for optimism for the future too. And I think we’ve made an excellent start on peaceful use of space with the Outer Space Treaty.

Although it’s frustrating that we don’t have warp drives or even the Star Trek “Impulse drive”, and easy ways to build habitats in space, I actually think it helps, that space is so hostile. Hopefully by the time we figure out how to live sustainably in space habitats, we also have figured out how to do it peacefully, or reasonably so. With competition of course, but more like the Olympic Games than WWIII.

Hopefully we can become more forward looking as we continue to colonize space. Perhaps the increased resources from space can help us to become more peaceful if we can handle it right.

If so we might well eventually have a chance to explore even our entire galaxy peacefully, and without harmful consequences to ourselves and other intelligent species that may exist in our galaxy. And if we meet ETs then they also I think would be ones that have figured out how to explore the galaxy in a similarly peaceful way.

THIS IS A GREAT FILTER IN THE FUTURE - ANY EXPANSIONIST ET MUST ALSO HAVE MINIMAL IMPACT - OR ELSE - WE ARE FIRST

I’m pretty sure there can’t be any aggressive exponentially expanding ET out there (such as we could become potentially) except by some amazing coincidence. That’s because unless they started on their expansion less than a million years ago, a tiny slice of the age of the galaxy, they would have occupied Earth and our solar system already, long before we evolved indeed, probably.

Any ET that managed to expand to a few star systems or to the Oort clouds, also I think can never stop expanding, short of warp drives. That's because if there are any of their species left anywhere in the galaxy that are expansionist, they will start up again, and take over from all the others that give up. How can that ever stop? Even if they started billions of years ago, they would still be at it, I think, even if most of them retreat into Dyson spheres or whatever it is they do, the few who don't would continue to expand through the galaxy.

So any "great filters" ahead of us have to operate before any ETs out there start on any major push of galactic imperialism.

I think the most likely reason is either

1. We are the first, so then it's our responsibility to make sure we take good care of our galaxy, leave it in a decent state for future generations and civilizations just as we would want earlier civilizations to leave it for us.
   
   If so, we must be exceptionally far sighted and careful as our decisions can reshape the entire galaxy for ourselves and other intelligent creatures in the galaxy for all future time. If we get this wrong, we can turn it into a never ending chaos that no-one will ever be able to calm down.
2. Or if there are other technologically advanced ETs, they have all found some way to explore the galaxy without major impacts on it, and without doing this uncontrolled galaxy cramming exponential expansion, or else they just “stay at home”. And the reason for that would be because the far sighted ones show restraint, eventually, maybe only after centuries or millennia of social development, or maybe quite quickly. And the ones who can't do that simply never get that far.

WILL WE BE A WEED OR A FLOWER IN THE GALAXY

The anthropologist Mary Dora Russell says:

'Anthropologists used to say that Homo sapiens was a unique and special species because we were the only ones who used tools, or who were self-aware, or had language, or passed culture to our offspring… Then we started finding out that chimps and dolphins and crows and African grey parrots and snow monkeys were making a mockery of our pretensions to uniqueness, so we’ve kind of shut up about all that in recent years.

If you want a nice reductive definition of our species, I could defend this: “Human beings are bipedal tailless primates who tell stories.”

That’s probably just as stupid as earlier definitions, but it’s catchier than my other version, which is

“Human beings are a dangerous, invasive weed species that has invented central heating, air conditioning, and food that can be stored for up to ten years, so not even a direct hit by an asteroid would likely make us extinct.”'

When nothing else matters, by Mary Dora Russell

I think that’s rather how I see the future of us in the galaxy if we just expand into it without foresight. But far worse than a weed on Earth. We’ve unnaturally made ourselves almost impossible to go extinct already by our technology and if we expand through the universe without evolving social breakthroughs of some sort, to catch up with our technology breakthroughs, I think we’ll become the ineradicable weed of the galaxy. But harmful to ourselves as much as to everyone else, and able to create even more dangerous replicators through our technology.

It's not just us. Our galaxy may well contain many non technological species, for instance intelligent fish-like or octopus-like creatures, living in the oceans of icy moons, or ocean planets, where they have no chance to develop control of fire. Or creatures that are just not very strong, and don't have good "hands" like us for manipulation, like parrots or crows. Even an elephant would have a lot of trouble building a fire and smelting metal. Ancient civilizations, perhaps advanced in mathematics, art, poetry, music, perhaps socially very advanced, yet without technology they would be especially vulnerable to a new technological species spreading out of control like an ineradicable weed through the galaxy. Out of all the intelligent creatures on Earth, I think only humans also had a decent chance of developing technology based on fire, even with intelligence. So if that's a good basis for generalizing, then the non technological civilizations universe wide may well outnumber the technological ones many to one. So, even a billions of years old civilization could still be highly vulnerable to a few centuries old civilization of technological ETs such as ourselves, could be.

I think any sensible ET will look at that possible future for themselves and the galaxy, and find a way to become a flower of the galaxy instead of a weed that will eventually choke all the species in the galaxy, including themselves. If they can’t see a way to a future like that, then if they have any sense, they just stay at home until they can. And if they haven’t the sense to do that, I think, perhaps, that they either make themselves extinct, or they keep destroying their own spaceflight capabilities, and get nowhere, until they develop some sense.

Let’s be one of the civilizations in our galaxy and universe that flowers like a beautiful flower.

Victoria amazonica (giant waterlily)

See also the section in my Case For Moon First: Further into the future, what about habitable planets around other stars?

This answer is partly based on extracts from my book.

See also: Robert Walker's answer to Will humans become extinct before we can colonize other planets?