You know what really grinds my gears? People who believe in aliens. I will approach this topic from three different worldviews: Biblical, Evolutionist, and Agnostic.
A Biblical Worldview
For a Christian, the belief in extra-terrestrial life (in reference to other intelligent beings, a.k.a. little green men, not simple microorganisms on Mars or wherever) is unnecessary. If there are any sort of extra-terrestrial beings out there in the wide universe, they do not have souls; they are not created in the image of God. They cannot be saved and live with us in heaven.
This is because God's plan of the fall and redemption of mankind is for just that - mankind. The Bible makes no reference whatsoever to any life outside of the planet earth and in understanding the panoply of Scripture, God is concerned with human life on this planet. I am not saying that He is not concerned with anything else besides human life on this planet, but in terms of the fall and redemption, He only works with human life on this planet.
A view which would see alien life as sinless (so they too could participate in heaven) would be ridiculous. Angels fell, man fell, why would aliens not? If a sentient being is not God, that being is fallible and will fall. God's justice would then demand a price to be paid for the sins of aliens. Some do theorize that Jesus went to other planets to be a sacrifice for other beings as well, but this is a complete twisting of Scripture. Even more, it is an absolutely nonsensical addition to Scripture which is completely without merit.
If there are alien beings out there, they are animals - lesser creatures than man. And I do not see God's revelation to us making room for the existence of life on other planets. If God wanted to make microorganisms or animals on other planets that's His business (although I hold this is unrealistic.) Regardless, it would take a fanciful imagination to assume that God is dealing with life outside planet Earth.
An Evolutionist Worldview
This is actually the least likely worldview to allow the existence of aliens. The evolutionist first has to say that life can spring from non-life. Even though they do unfortunately hold this assumption, they then have face the astronomical odds against this happening naturally. (Setting aside the fact that the odds of this happening are simply zero, they at least have to face the overwhelming odds against this happening, regardless of how much time the universe has provided this opportunity.)
Even though it happened to come about on this planet, as they claim it has, it would have to happen again on another planet for alien life to be possible. If life originated on some other planet and the organisms were somehow hurtled through space to earth and other planets, and that is why beings can exist on multiple planets, then evolutionists would say that the common tendency is for simple organism to evolve and adapt to their environments - in a universe which all things tend toward chaos.*
Simply, if there are aliens on another planet, life sprung from non-life on that planet as well, defying even more astronomical odds, and the beings evolved. The concept of there being aliens on other planets, especially little green men which can travel to ours, the possibility that the unbelievably impossible odds of spontaneous life were defeated multiple times, is thoroughly laughable. Going several steps forward, things like Star Trek and Star Wars which have multiple intelligent races have to be kept strictly as science fiction. That this would have to even be said in today's world is regrettable.
*The craziness of a species adapting to environments toward greater complexity is another topic entirely - maybe someone else here would want to tackle it some day. How many generations of dogs thrown into the ocean will it take for them to finally figure out how to grow gills? I know the evolutionist would say that gradual adaptations into gradually changing environments is how it was done, but simple reason can still shoot down the concept of macro-evolution. That, however, is not the purpose if this post.
An Agnostic Worldview
For the purposes of this topic, I will consider an agnostic as one who believes that there could be divine out there, but not necessarily the God of the Bible. The general belief in mysticism, ghosts, angels, gods, and such - this way, anything is possible. Everything from the world resting on the back of a turtle, the Greek pantheon of Gods meddling in human affairs, Scientology, a careless creator who set evolution into order, etc.
It is in this view that the possibility of aliens is actually completely reasonable. Not only is it reasonable, it would be unreasonable to figure we humans are the only intelligent beings in the universe. Star Trek and Star Wars might as well be possible. This is obviously because the gods could go on creating new life to their hearts' content.
I know more reasons can be given by others to support my view. But in summary, it is unreasonable for a Biblical worldview to entertain the existence of aliens. It is also unreasonable in an evolutionist worldview. Only in an agnostic worldview is the existence of aliens any shade higher than practically impossible.