Discovering aliens would neither prove nor disprove the existence of God, but it would raise all sorts of problems for the specifics of many existing religions. I don't know enough about other religions to speak for them, but I'm a lapsed Catholic so I can name a few problems it would raise for The Church.
Do all intelligent organisms have souls? If so, how intelligent do they have to be in order for God to give them souls?
Do space aliens have original sin? From what I understand, sin came into the world after the Devil tricked humans into defying God by becoming self aware. Does this mean that space aliens cannot be self aware without sin? Or are the souls of space aliens somehow different from the souls of humans? Given the age of the universe, space aliens could have evolved to the level of sophistication needed to consciously choose to sin billions of years ago. Did the Devil make sinners out of them too? How long ago? Since intelligent life very well may have been around since billions of years before there were humans. Has the Devil been corrupting God's children for that long? If he has, how has God not figured out how to stop one rogue angel from ruining his plans in all that time? Is there more than one devil, or were all sinning beings corrupted by the same one? Are there any alien creatures that were tempted by the Devil's promise of godlike intelligence and resisted?
Do space aliens have their own saviors? When Jesus was killed, did he die to save humanity from its sin, or all intelligent beings? If Jesus did die to save all intelligent beings from sin, how long have space aliens been waiting to be saved? If Jesus died to save all intelligent beings from their sins, are humans obliged to spread the Gospel to the rest of the universe? If other species have their own saviors, were they all Jesus, or did God have more than one son? Has Jesus been crucified a billion times on a billion worlds to save a billion species? Does Jesus have a billion brothers? Can Jesus be a billion people at once?
Catholics believe that the Holy Virgin is the bride of god. Does God have space alien wives too, or are humans special like they are in Mass Effect? If God has other wives, did Mary know about the other wives before she and God got married? If not, how did she react when she found out?
If there are other intelligent beings in the universe and they don't look like us, what does it mean to be created in God's image? Again, are humans just God's favorites? Does God's creation of humans in his own image refer to something more fundamental than our physical bodies?
The discovery of alien beings would raise all of these questions and more, but The Church would not necessarily have to answer any of them to survive. After all, The Catholic Church has already accepted that the Earth is probably 4.5 billion years old and that humans have most likely evolved from more simple organisms, but as far as I know, they have not answered the question of how far back the creatures modern humans are descended from acquired immortal souls.