Beloved, we are God's children now; what we will be has not yet been revealed. What we do know is this: when he is revealed, we will be like him, for we will see him as he is (1 John 3:2).
Many early church fathers taught deification or theosis (see the quotes at that link), but my favorite teachings on it come from C. S. Lewis. In the essay "Man or Rabbit?" found in God in the Dock, he wrote:
The people who keep on asking if they can't lead a decent life without Christ, don't know what life is about; if they did they would know that ‘a decent life' is mere machinery compared with the thing we men are really made for. Morality is indispensable: but the Divine Life, which gives itself to us and which calls us to be gods, intends for us to be re-made. All the rabbit in us is to disappear -- the worried, conscientious, ethical rabbit as well as the cowardly and sensual rabbit. We shall bleed and squeal as the handfuls of fur come out; and then, surprisingly, we shall find underneath it all a thing we have never yet imagined: a real Man, an ageless god, a son of God, strong, radiant, wise, beautiful, and drenched in joy.
And in Mere Christianity, Lewis also said:
The command "Be ye perfect" is not idealistic gas. Nor is it a command to do the impossible. He is going to make us into creatures that can obey that command. He said (in the Bible) that we were "gods" and He is going to make good His words. If we let Him -- for we can prevent Him, if we choose -- He will make the feeblest and filthiest of us into a god or goddess, dazzling, radiant, immortal creatures, pulsating all through with such energy and joy and wisdom and love as we cannot now imagine, a bright stainless mirror which reflects back to Him perfectly (though, of course, on a smaller scale) His own boundless power and delight and goodness. The process will be long and in parts very painful; but that is what we are in for. Nothing less. He meant what he said.
So there is room for traditional Christians to believe in becoming gods. If that's the case, what's the difference between what Christians traditionally have believed and what Mormonism teaches now?
Traditional Deification v. Mormon Exaltation
Here is an excerpt from a mock dialogue in The God Makers (a notorious anti-Mormon film), which seeks to illustrate the LDS doctrine of exaltation (again, emphases mine):
"Do you realize the implications of this doctrine as far as you are
"I think so. If God became God by obedience to all of the gospel law with the crowning point being the celestial law of marriage, then that's the only way I can become a god."
"But I thought godhood meant freedom. If I have to do things to become God, am I really free?"
"You have got it wrong. It was the Savior who said, ‘If ye continue in my word,' that is, obey the law, ‘ye shall know the truth, and the truth shall make you free' (John 8:31, 32). So by obedience to law, we learn truths by which we become free -- but not free from the law. Can you see that?"
"I think so. I can be a god only if I act like God."
"Exactly right. Can you imagine the state of the universe if imperfect gods were allowed to spawn their imperfections throughout space, if beings who did not have law under their subjection were free to create worlds?"
"I guess that would be pretty disastrous. But I'm not sure I see why celestial marriage becomes the crowning apex of this progression. Marriage doesn't seem directly related to the creation of the universes."
"Oh, but don't be limited by your mortal perspective. God himself has declared his own reasons for existing. Remember, he said, ‘For this is my work and my glory...'"
"I see his purpose is ‘to bring to pass the immortality and eternal life of man'" (Moses 1:39).
"Which involves giving birth to spirit children and setting them on the road to exaltation. And if that is to be done, you must have an exalted man and...'"
"An exalted woman."
"Exactly, an exalted man and woman who have been joined together in an eternal marriage. If this man and woman were obedient to all gospel laws except celestial marriage, what would be the result?"