Recently, in addition to working on my dissertation, making a new set of fold-up paper minis (just need to format the pdf), and getting ready for a vacation, I've been watching Neil DeGrasse Tyson's Cosmos: A Spacetime Oddysey. I missed it two years ago when it first aired. And of course, my mind is now thinking of lots of interesting ways to set up a galactic scale sci-fi RPG campaign.
One good place to start for assumptions about extraterrestrial life in the universe is the Fermi Paradox, and the Great Filter hypothesis that goes with it. Are you familiar with it? If so, you can skip the next paragraph. If not, here's the Fermi Paradox in brief (and click that link for an excellent in-depth discussion of it if you want to know more):
If the estimated number of stars in the universe, the estimated number of planets around those stars, and the estimated chances of life spontaneously arising on any planet with suitable conditions are what scientists believe them to be, even at the lowest, most conservative numbers, our universe must be bursting with life. And given the 13.5 billion or so years since the Big Bang, there must be many intelligent species out there besides us. Yet (this is the paradox), we can't detect any signs of them (or have we?). There are several explanations for why this might be so, including the idea of the Great Filter, an event that makes it highly improbable that life will advance to not only intelligence, but to super-intelligence levels needed to colonize other planets.
So that's the Fermi Paradox in a nutshell (and I'm sure I've introduced some error into the concept by such a brief recap, so if you're interested, click that first link above and enjoy). And the various hypotheses that seek to explain it can give your sci-fi campaign some interesting twists. The best thing is, they're fairly setting neutral, unless you're planning to use a popular sci-fi franchise like Star Wars, Star Trek, Babylon 5, Firefly, what have you.
The first way to solve the Fermi Paradox is to suggest that there ARE NO HIGHER CIVILIZATIONS (we aren't quite there yet in real life). In other words, the Great Filter is behind us. Let's look at some conceits that could inform your sci-fi campaign if this were the case:
1. There is no life in the universe except that on Earth.
The Earth is the only planet where there is life. The Great Filter is the formation of life itself.
You could set up a campaign set on Earth in the far future, just with lots of fun high tech toys, but otherwise more or less your typical human drama. Or you could set up an explore/terraform/colonize setting, where the PCs are faced with this challenge - to seek out suitable worlds for colonization (exploration and bottle-city human drama on their ship), or to be among the terraformers or colonists (a survival against nature game).
The Bible (or whatever creation myth you choose) was correct after all. Considering Einstein's Theory of Relativity, if you choose the Earth
as your frame of reference and consider celestial motion in a certain
specific way, the universe DOES revolve around the Earth. Could the revelation of our unique status in this universe propel humans to embrace Scripture and form future theocracies? This might step on a few real world toes among players, so use this idea with caution.
2. There is life in the universe, but we are the only intelligent life.
Maybe we're the first and more will come later, or maybe others existed before and were wiped out. The Great Filter is behind us, or else where we are now in the early 21st Century (nuclear or environmental devastation of the planet, overpopulation leading to catastrophe, etc.), and humans just squeak through.
In this case, you may have a campaign set up where the PCs are among colonists sent to settle other habitable planets with no need of terraforming. Of course, the life forms on the other planets will be different, interesting, and often dangerous. If you go with a "we're the first" premise, then you get exploration, cataloging and survival on alien worlds. If you go with a "no others survived this far" premise, you can add in exploration of the ruins of lost alien civilizations to the above. [Stars Without Number uses this conceit as its default, with options to add in alien species if the GM wishes.]
3. There is other intelligent life, but they're only just as advanced as us, or less so.
Conditions in the universe have been such that we're leading the pack as far as super-intelligent civilizations go. The Great Filter is behind us, and behind several other civilizations. And we were just too far away to detect each other's presence until the advent of FTL, warp engines, star gates, or however you want to move people around interstellar distances easily in your campaign.
In this universe, it will be a game of planetary exploration as in #2, but with First Contact opportunities, and the interspecies ice-breaking games that come with that contact. There will be a limited number of player races (the few super-intelligent species), but there could be any number of intelligent but non-advanced civilizations on other planets if the Great Filter is the industrial/nuclear age transition. [Star Frontiers uses this conceit, with only five star-faring races, all of comparable tech levels.]
Finally, it could be that humans form the first Type II civilization and are the first to colonize other planets. If there are other intelligent but not yet advanced alien species out there, then it may be the job of the PCs to study them passively (a la Star Trek's Prime Directive), or to conquer them, or to make peaceful contact with those we can and enlist their help to pacify those we can't make peaceful contact with (although if we're the only star-faring race, there would need to be some sort of situation like James Cameron's Avatar, with its unobtanium, necessitating our even bothering with the hostile aliens).
The second way to solve the Fermi Paradox is to suggest that ADVANCED ALIEN CIVILIZATIONS ARE OUT THERE, BUT FOR SOME REASON WE CAN'T DETECT THEM. We are probably past the Great Filter (although not necessarily), if a Great Filter exists, but by design of the aliens, limits of our technology, or cosmic chance, we (us, real 21st Century humans, not your campaign) just haven't encountered these other civilizations yet. These also give use plenty of fodder for designing a campaign.
4. Advanced aliens visited Earth long, long ago, and just haven't been back since then.
This idea, the Ancient Astronauts theory, is of course a popular one now. Maybe the aliens seeded life here, then forgot to return (or were wiped out by enemies). Once humans gain interstellar travel capabilities, the campaign could be one of piecing together the mysterious clues to the origin of life on Earth.
Or maybe the aliens finally return, and bring humans into the galactic (or intergalactic) civilization. This way, you could play as modern humans, out exploring the galaxy for the first time, but with guides along the way. Alternately, the seeding species may have put us here for a purpose (crops, slaves, lab rats) and the PCs have to resist the alien overlords. Wars of humans vs. alien invaders is probably not a trope I need to go into great detail here, I'm sure you've got a handle on this idea.
The third idea related to this is that our ability to get past the Great Filter, or simply to develop to a Type II and/or space-faring species is some sort of test. Once we pass the test, we become citizens of the galaxy. The campaign will again consist of the players having to negotiate strange alien customs while exploring the galaxy.
5. Most of the galaxy has been colonized by a single Type II or proto-Type III civilization, but the Earth is in a galactic backwater.
This is the basic concept of the Hitchhiker's Guide to the Galaxy series. There's just nothing on Earth to interest the aliens, so why would they bother coming here? As with the Hitchhikers series, maybe the aliens have just stared paying attention at the time the Great Filter hits (whether that be Vogons or something more serious is up to you), and the PCs are the few survivors taken in by the aliens at the last minute. And it need not be silly as in the Hitchhiker books.
Or maybe 'Space Noah' leads a small group of survivors off of Earth just in time, and when they escape destruction, they find an advanced civilization has already pretty much taken all the good planets. This could then be a sort of Battlestar Galactica type game, where the few survivors of Earth need to explore, fight, negotiate, or run from the galactic civilization.
It could also be that there's no imminent disaster for Earth, but a select few, the PCs, by design, chance, or fate, have been taken from Earth (or find a one-way ticket off through science). Maybe they want to get back, and that's the campaign -- survive in the galaxy long enough to find a way back to Earth. Maybe they're happy with their lot in life, and have no desire to return to Earth (like Star Lord in Guardians of the Galaxy). Whether galactic murder-hobos or scientific explorers, the PCs can enjoy their status as "oddities" among the galactic civilization(s).
6. There are several Type I and Type II civilizations that vie for control of the galaxy.
This one, again, maybe doesn't need a lot of explaining. There are two or more "galactic empires" that compete for habitable worlds to colonize, or lesser species to exploit, or just have some sort of beef with each other that prevents them from coexisting (the desire to become the Type III civilization of the Milky Way, maybe). Humans could be one of these empires (and the campaign would be similar in some ways to Star Trek, with the Federation, Klingons, Romulans, Borg, etc.), or we could be caught in the crossfire once we're finally noticed or make ourselves known. Maybe the aliens notice the potential of humans, and they are vying to make us allies. Maybe they notice the potential in humans, and are trying to wipe us out before we become yet another threat.
7. Physical colonization of planets is unfeasible, and interstellar travel is a rarity.
In this situation, the cost outweighs the benefit for galactic colonies. If Type I or Type II civilizations are utilizing all potential energy sources of their planet/star, why bother going somewhere else? Maybe the civilizations come into contact by some form of FTL communications system (the ansible of the Ender books, or subspace frequencies of Star Trek, for example). We can learn from them, they can learn from us, in some sort of galactic Google Hangouts sessions, but never shall we meet...unless, a crazy group of humans (the PCs) decide to build an FTL ship just for shits and giggles and set out to meet these other peoples of the galaxy! This could be fun, because each planet visited would then open up the opportunities for the players to play a member of an alien species (they've got their own crazy weirdos as well).
8. Smart civilizations don't advertise.
There may be predatory alien species (the lizard folk of V, the whatever they are from Independence Day, etc.). The smart civilizations don't go around making unnecessary signals that would draw their attention. There's a lot of potential with this idea. Humans may have made the mistake of attracting unwanted attention (war against alien invaders) which then leads to the need to find extra-terrestrial allies -- not easy when they don't want to be found. This would be a combination of survival/war, and exploration/mystery solving.
Maybe WE are the predator species, and we need to hunt down and locate the inhabited worlds for some reason. I think most players enjoy the occasional game where they're the bad guys, but this obviously wouldn't be the game for everyone.
There could be a Type III civilization that keeps others down, swatting the flies before they can become a real threat. This could also be interesting, as the PCs would be facing a vastly superior foe. How do you defeat a galaxy-conquering species that is millions or even billions of years more advanced technologically? Do you make this an Ewoks vs Empire type situation for the players? Do the PCs just try to find a place to hide, searching the galaxy for an even more backwater world to relocate to once Earth has been discovered?
9. The government is covering up the evidence.
Maybe there are thousands of extraterrestrial civilizations, maybe there's one Type III super-civilization, or something in between. No matter what, the various world governments (or at least the great powers) are suppressing that knowledge. While many scientists might scoff at this in real life, it has vast potential for gaming. Of course, you could go the X-Files route, with the players trying to uncover the alien conspiracy. Or you could go the Star Gate route, with the PCs being the agents of the government(s) who go out among the stars to deal with alien threats and treat with alien allies.
10. The aliens are all around us, but we just can't detect them.
Maybe their technology is so different from ours that we can't detect them because we're looking for the wrong things (and vice versa). Maybe their form of life is just so alien to ours that we wouldn't even be able to notice them (non-carbon based, for example) if we were standing next to them.
In the first case, the PCs may be in for a surprise first contact, thinking the campaign was something along the lines of suggestions 1 and 2 above, only to meet a twist along the way. This would switch the explore/survive campaign into a study/befriend campaign. Or an alien war, those are always fun, too.
In the second case, maybe the thrust of the game is to learn about these truly alien life forms, and eventually find some way to make contact with them. There's a lot we could learn from a species so different from us that we wouldn't even likely be competing for the same planets (unless one or both of us are into terraforming!). I could see a game starting out where a planet that we had detected as Earth-like was not (terraformed by the aliens to suit their biology) by the time a generational or hypersleep colony ship could arrive. Solve that mystery, players!
There's more that can be gleaned from the Fermi Paradox and the idea of the Great Filter, these are just a few. Feel free to chime in with others you might think of (or ways to improve my ideas) in the comments!