I think it is unlikely that there are aliens, or if there are it is no concern of ours.
Here are a few points to consider:
- The Bible is silent on this issue - beings from other parts of the universe are not mentioned (though beings from outside the universe - angels - are!). This means that they might exist, but it means that they might not. You can't make a call either way from the bible.
- If they don't exist, how do we reconcile the massive "waste" of space that the universe and all that is in it appears to be? The Bible says that "The heavens declare the glory of God" (Psalm 19) so perhaps He intends to show something of His nature and power through such a display of almost endless creation. The incredible order and beauty tell us that there is an intelligent and artistic mind behind all of existence, and the sheer energy required to form all of the mass in the universe (consider E=mc^2) speaks of a vast and powerful God. I think that a lifeless universe (Earth excepted) has more than enough purpose to satisfy.
- But the Bible is still silent on this issue! Yes, but that indicates that, even if aliens exist, we are unlikely to ever encounter them. The lack of instructions in how to deal with them (if they did arrive) means that God doesn't expect us to meet them. And if you know anything about the extraordinary vastness of space, you know that it would take many, many lifetimes to ever get anywhere for any being that could travel across those vast and empty chasms between worlds. The speed of light is a fundamental limit, and there is no known way to break that, though I guess it might be possible in the future which leaves a tiny glimmer of hope for alien enthusiasts. However...
- Most alien enthusiasts are actually alien crazies (no offence intended, but that's how the type of person I'm about to describe comes across). So focused on the "certainty" of the existence of aliens because it gives them a sort of hope and meaning. Something is bigger in the world than their mundane problems and daily struggles. Those who have had "visitations" are usually those who have experimented with the occult (knowingly or unknowingly), and are likely to have experienced some sort of demonic (dark angelic) encounter and have mistaken it for an alien abduction or similar. Demons aim to deceive in any case, so don't feel too bad if this is you...
- If aliens did exist, they would be fallen sinful beings, as a part of a fallen creation, who are subject to God's laws. If God has revealed Himself to them with special revelation (like the Bible) it will show that He has the same character and focus for those who he created. His merciful nature, but also his desire for justice, will be wherever He is. And God is everywhere in His vast Creation. If aliens exist, they will have to face God at The Judgement to give account for their life's deeds. And if they don't have a saviour to take the punishment for their sins, as we have in Jesus Christ, then they will take their punishment for eternity in Hell too.
If you are not a Christian, you can go on believing in aliens if you so desire. However, now you know that there is an answer to this issue from the Bible, i.e. God doesn't want us worrying about the possible existence of aliens because even if they exist it probably doesn't matter.