In this short discussion I brainstorm whether rational beings from other planets can exist biblically: little green men, Boltzmann brains, or anything else as intelligent as us.
The existence of life originally from another planet has strong implications of evolution. This is already an indicator for many who don't accept evolution to deny the possibility. It would be a little pointless for God to create, say, an unreachably distant planet inhabited only by microbes, given that He made the ecosystems on Earth for man.
Additionally, if there are other beings, the question of their redemption becomes a little confused: do they have souls and are they saved like us, not being descendants of Adam? Why are they under the curse?
This last question can be answered easily: Adam's curse extended everywhere, throughout the universe: we see supernovae, black holes, gamma ray bursts and other signs of "decay" (Rom. 8:21-22).
In the Middle Ages, the redemption of these other beings was the original objection to not only the existence of aliens, but people outside Europe, Africa, and Asia - "antipodes", or men whose feet faced the opposite way. Vergilius of Salzburg, an 8th century bishop, was nearly excommunicated for this by Pope Zachary, saying:
if it shall be clearly established that he professes belief in another world and other people existing beneath the earth, or in [another] sun and moon there, thou art to hold a council, and deprive him of his sacerdotal rank, and expel him from the church. [Monumenta Germaniae Historica, Epistolae Selectae, 1, 80, pp. 178–9; translation in M. L. W. Laistner, Thought and Letters in Western Europe, pp. 184–5.; see also Jaffe, Biblioth. rerum germ., III, 191]
The issue with antipodes was that they couldn't have descended from Adam if they were all the way on the other side of the world, with the assumption that nothing like the Bering Strait could have existed (why one should never presume out of ignorance, no matter how old and well-established a tradition, be it scientific such as the geography of the world back then, or religious such as the near excommunication of Vergilius here).
We now know that not only did "antipodes" exist, but that they were completely human. But that would obviously not be the case with extraterrestrial "men". It would be a little more than bizarre to suppose that God had Jesus die for them too somehow, or again on their world(s), or that He decided some other way, so these two objections remain: (1) how would they be saved?; and (2) why make them, at least why on another world(s)?
II. Redemption and Purpose
I feel there is some possibility for biblically accepting the potential existence of aliens. Regardless of whether a Christian accepts evolution or is a creationist, there's good arguments for how and why God would allow extra terrestrials' existence.
The question of redemption can be answered in two different ways. In all likelihood aliens would be just very smart, soulless creatures - like animals or robots. If I made a group of knowledgeable robots and left them on a desolate planet, it would be the same thing if they somehow came into existence on their own. If an extra-terrestrial tornado swept a bunch of metals enough times and made the first self-aware robot, an electronic Adam, who knew how to make more copies of himself.
Most of our knowledge, function, power, and activity is physical and has nothing to do with anything metaphysical: habits + instinct. If animals such as gorillas can learn sign language, and would actually be able to talk like us if it weren't for something like 1-3 base pair differences in their DNA for their tongue, then I don't think it's impossible for aliens to exist in the classic UFO version (minus the telepathy and what not I guess). Some animals like some parrots can talk, of course, so we can't really consider ourselves unique on those points.
If extra-terrestrials are answerable for their sins like us and angels/demons, then is it impossible that there was some other way God could forgive them than accepting Jesus? After all, none of the Old Testament righteous men knew specifically of Christ, and arguably many others who had never heard of Christianity.
The difference is that the E.T.'s wouldn't be descendants of Adam. If someone accepts evolution, this is not a problem. But even if they don't, if the whole universe suffers because of Adam (Rom. 8:21-22), then perhaps God does not need to be a legalist and can allow them to repent (cf. something similar hinted in Heb. 7:2-3, 4-10, 11-28 (where alternate priesthood rules are metaphorically given by a logical rationale); Rom. 5:12, 18; Rom. 11:17-24; Gal. 3:7, 22-24, 28-31). The early Church actually had to convince many of its Jewish members that Gentiles could be saved since they weren't children of Abraham. Paul struggles to connect the two understandings for his audiences (Galatians 3; Romans 4; 9:6ff) so why does Adam have to be the limit? Maybe God can forgive them another way. Muslim arguments against Christianity have sometimes focused on why God needs a sacrifice to forgive: after all, the individual Christian simply needs to believe with actions as well as words.
And why make them? This objection has even less weight. Originally the possibility of the existence of Amerindians (and Aboriginals, Polynesians, etc), or "antipodes", was denied because why would God make them so far away from the possible knowledge of Christ (perhaps ever)? But the same argument can be made about anyone more than 1000 miles from Israel. The elderly Simeon (Luke 2:25ff) was happy to merely see Jesus as a child. He didn't know him any better than that before presumably passing away soon after (Luke 2:29), nor would he know about Jesus' death and resurrection at the time of his death. In other words, men on other planets can entertain themselves quite easily the way the "antipodes" did for millenia before 1492.
Verses like Acts 4:12, Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved, may seem to be the final word. Although the Apostle uses words like "no other name given" and "to mankind" as if another name to some other race could, the intent is that Jesus and his purpose are unique.
But we should always beware of anthropocentrism: it's what made geocentrism an unnecessary standard model of cosmology for millenia, and it wasn't until the 1920's when galactocentrism, the idea that our galaxy is the whole universe, was abandoned: with many good arguments for the existence of other galaxies unaccepted by scientists until Hubble, merely because they couldn't conceive of it.