In John 10:16, Jesus says that "I have other sheep that do not belong to this fold. I must bring them also, and they will listen to my voice. So there will be one flock, one shepherd." While I doubt that Jesus was referring to life on other planets, the discovery of extraterrestrial life would simply mean that our understanding of the "wideness of God's mercy" would have to be broadened to include all creatures. If we believe that our God is the sovereign ruler of the universe, then God's love would be extended to all beings on all planets. It would be consistent with Jesus' teaching to his disciples in Acts 1:8, that "you will be my witnesses . . . to the ends of the earth." The discovery of life on other planets would merely broaden our understanding of the limitlessness of God's love and our Lord's desire to include all creatures - on Earth and anywhere else - in God's loving embrace.
The Talmud states "God flies through 18,000 worlds." Since they require His providence, we could assume that they are inhabited. We find in Psalms 145, "Your kingdom is a kingdom of all worlds." However, these also could be referring to spiritual worlds. Where we find the existence of extraterrestrial life most clearly supported is in the Zohar. Widely considered the most important work of Kabbalah, the Zohar is a mystical commentary on the Torah, the five books of Moses. The Midrash teaches there are seven earths, the Zohar clearly states that the seven are separated by a firmament and are inhabited. Although they are not inhabited by man, they are the domain of intelligent creatures. There may even be other forms of intelligent life in the greater cosmic universe, but summarily all such life-forms do not have the GodForm/Image of free will, and therefore do not have moral responsibility. Within Halakah, Jewish law, this is the key. A b'nai mitzvah, one who reaches maturity, is one who accepts responsibility - specifically, the moral ability to choose between good and evil. Since in Judaism, man is the apex of creation because his creation genesis is in the "image" of God, through this ability of "free will" he is but potentially a little less than God. Indeed, freedom of will is hardly observable, the inner secret life of the human being. The general Rabbinic consensus bottom line is it would have little impact on Jewish law. What an experience of contact would allow us is a deeper appreciation and gratitude for the wondrous abilities in the freewill space of action-reaction we all have in the marvelous world condition we currently inhabit, but that is freely available in the here and now. Shalom.
If life were discovered on other planets, the impact, in my view, would be to enhance our awe and praise of the God who has revealed Godself in Jesus. That God would enter into humanness to reveal "a heart" of unbounded love that can only call forth from us a response of ever growing love. That God's love would become incarnate in the manner of living a fully human life and showing what Jesus described as "no greater love" than to lay down one's life for one's friends, reveals a God of such magnificence and munificence, a God who, almost incredibly, only wants to share God's own life with us, that we would believe that such a God only wanted more people "to love and be loved by" in creating life on other planets. Thus, I believe that such a discovery would only enhance religious belief.
It would be exciting to discover life on other planets, but it would not have any impact on my own religious beliefs. Christianity is based on friendship with God, not any particular theory about extraterrestrial life. My faith is based on following Jesus in this world and trusting him to lead me into life on the other side of death. It doesn't disturb me in the least to imagine that God might have created a universe in which there is intelligent life someplace else, too.