Possibility 1: They Conquer Us
Given the fact that the universe is nearly 14 billion years old, aliens arriving in our solar system might be part of a civilization many thousands or millions of years older than our civilization. So it is quite possible that a single starship could have the power to conquer our entire planet. One can easily imagine various approaches that aliens might take. A few nuclear bombs could be exploded in the upper atmosphere of the world's largest countries, causing an electromagnetic pulse (EMP) that would wipe out most of the power system and electronics of major nations. A few super-advanced self-reproducing robots could be landed on our planet, and they could then start making copies of themselves, using as raw materials metals swiped from cars on the street. Before long there might be a huge army of such robots, ready to attack us. Or a specially designed biological plague could be used to terrorize the world into surrendering. A very advanced alien civilization might even have mind-control techniques that would destroy our will to resist them. The end result might be the forcible bringing of our planet into some kind of galactic empire that the aliens controlled. The conquest of our planet might be just another in a long series of conquests made by such extraterrestrials.
Possibility 2: They Enslave Us
This is like the previous possibility, but even more radical. Under this scenario, the aliens make everyone on Earth a slave. The aliens might do this if they wanted to colonize our planet, but regarded it as being a disgusting eyesore. They might then wish to make us all slaves so that we would get to work cleaning up the mess we have made here on Earth, making it into a place more suitable for their colonization. Perhaps they might want a lovely, unspoiled planet to colonize, and they might order us to begin dismantling all of the ugly strip malls and highway billboards and fast food restaurants. Or they might put us to work building the type of structures that they preferred to live in, which might use some strange alien architecture. This enslavement possibility does not seem to be very likely, because super-advanced aliens would presumably have mastered robotics, and could use robots to accomplish what they wanted on Earth without using human slaves.
Possibility 3: They Exterminate Us All
This is like the previous two possibilities, but even gloomier. Under this scenario, the extraterrestrials arriving in our solar system decide that there is no way that they can successfully share our planet with humans. So they decide to simply wipe us out altogether. They might be able to achieve this goal by introducing specially designed plagues designed to kill everyone. They might also make use of specially designed nuclear weapons designed to kill without leaving much long-lasting radiation (perhaps something like the neutron bomb envisioned in the 1980's).
After the aliens got rid of all humans, they might also decide to get rid of all of our buildings, which could be done by an army of robots. Or they might simply decide to make use of all of the structures we built. The latter case would lead to a very strange situation. Imagine a New York City of the future where no humans live but where thousands or millions of extraterrestrials live.
Possibility 4: They Absorb Us
This possibility could be called the Borg scenario. It could be that the beings arriving from another planet are united in a kind of group mind or collective consciousness. It might also be that they want to absorb us into this group mind. Once we become absorbed, we would think as they do, and feel as they do. We would then live only to serve the will of their group mind. This might be the most effective way for the extraterrestrials to accomplish the equivalent of the enslavement of humanity.
Possibility 5: They Eat Us
In a classic episode of the television series The Twilight Zone, aliens arrive from the stars, bearing a book entitled To Serve Man. It turns out the book is a cookbook, and the aliens are interested in serving man broiled, baked, or stir fried. This scenario made a great television episode, but isn't very likely in real life. An alien life form would probably have a genetic code entirely different from ours, and would be unlikely to be able to eat any people or any other mammal on our planet. It also seems that whatever type of meat they desired, they would be able to artificially synthesize it, rather than going to the trouble of getting it from earthly organisms.
Possibility 6: They Watch Us Protectively
In this scenario extraterrestrials arrive in our solar system, and then simply observe us discreetly. Perhaps their goal is to just watch us and make sure we don't destroy ourselves. Some UFO believers think that this scenario is now occurring, and that when UFOs are seen, people are seeing extraterrestrial vehicles.
Possibility 7: They Bless Us With Cosmic Gifts
Call this the Santa Clause scenario. In this scenario extraterrestrials arrive in our solar system, and make their presence known. Maybe they land a vehicle on the White House lawn very quickly. They then begin to share some of their godlike technology with us. Maybe they give us the cure to cancer, or maybe they give us the technology to reverse aging. The world then embraces the cosmic visitors as forces of benevolence.
Possibility 8: They Mate With Us
A scenario in which extraterrestrial visitors mate with humans seems to be very unlikely. As all life on Earth is based on a distinctive genetic code that would be unlikely to be repeated exactly on other planets, there would not seem to be any possibility that extraterrestrials would be successful if trying to breed with humanity. Nor does it seem that beings from some greatly superior species would have any interest in breeding with humans, which they would be likely to regard as a greatly inferior species. They would probably also have a physical appearance greatly different from ours, meaning that they would probably be repulsed by the idea of mating with humans, just as a human might be repulsed by the idea of mating with a very different type of species such as an octopus.
Possibility 9: They Want to Convert Us
Another strange scenario is that extraterrestrials might arrive and want to convert us to some cosmic religion that they were trying to spread to as many planets as possible. It is hard to convert anyone to a different religion, but aliens might have all kinds of mind-control techniques that might make it easy for them to convert us to their strange alien creed.
Another scenario is that extraterrestrials arrive and offer us some kind of membership in an interplanetary society or empire. Perhaps it might be an attractive offer to join a galactic confederation or galactic society similar to the United Federation of Planets depicted in Star Trek, or the galactic Republic depicted in some of the Star Wars movies. Or it might be a less attractive “make you an offer you can't refuse” type of offer to join a galactic empire, giving up much of our independence and freedom. In the latter case there might be various mind tricks to make us think that we are getting a good deal rather than being subjugated, like the arrangement where Hitler set up the Vichy France government in conquered France.
Call this the “schoolmarm scenario.” Under this scenario the super-advanced extraterrestrials arrive, and take up the task of teaching us ignorant, silly humans the deep cosmic truths the aliens have acquired over the eons. This might be a slow process taking many years, and might require them to establish universities on our planet. This is an interesting possibility that I'm not sure has ever been explored in a science fiction story.
This would be the most humbling of all scenarios. Extraterrestrials could arrive in our solar system, and decide that our puny little civilization is quite unworthy of their attention. They might then snap a few photos, take a few samples, and leave the solar system quickly. This would be an ego-deflating event for human hubris. It would slowly dawn on us that we are mere tadpoles in the great ocean of cosmic life.