"I am God" if a human said it, truly believing it, that is. I know there are concepts like those of Brahman and Paramatma which indicate a unity of divinity, as well as the Sanskrit phrase "Tat twam asi" and the Bhagavad Gita's message (which seems to center a lot on the individual)...but do these add up such that the phrase "I am God" has some validity?
If you want to know whether the phrase "I am God" has validity in Hinduism, that exact phrase is present in the Brihadaranyaka Upanishad (Nikhilananda's translation):
(Note that Brahman is only one possible translation of the word "god"; see my answer in Meta.) Now the question becomes how to interpret the passage. Some might interpret it as saying that the only thing that's keeping you from "becoming the universe" is that you don't realize that you're already the Universe. Others would say, however, that the passage means that you used to be Brahman and that you can become Brahman after you realize your former state, but that you're not Brahman right now.
The Hindu religion doesn't have a single position about the relationship between Jivatma, the individual soul, and Paramatma, the supreme soul or soul of the gods. Rather, different sects of Hinduism, like Advaitam, Dvaitam, and Visishtadvaitam, have differing views on the question.
According to Adi Shankaracharya's philosophy of Advaitam, Jivatma is already identical to Paramatma, he just doesn't realize it yet because he's in the illusion of Maya. Madhvacharya's philosophy of Dvaitam, on the other hand, posits that Jivatma and Paramatma are totally seperate, and that the best the Jivatma can hope for is to get into more elevated state, never actually becoming one with Paramatma, as I discuss in this answer. And Ramanujacharya's philosophy of Vishistadvaitam (the philosophy of Sri Vaishnavas like myself) advocates a compromise position, where there is larger whole but within that whole there is some division, akin to the relationship between a fetus and a pregnant woman; the fetus is a part of the pregnant woman's body, yet it's not the same as the pregnant woman herself.
And there are other philosophies like Chaitanya Mahaprabhu's Achintya Bheda Abheda, where there is simultaneous oneness and difference, but where the coexistence of unity and plurality is beyond Man's comprehension.
So to sum up, while the phrase "I am Brahman" does occur in Hindu scripture, the larger question of whether you are Brahman right now is one that is hotly debated amongst the different sects.
Does the phrase "I am God" have some validity?
Yes, it has. Because this phrase "aham brahmāsmi" is not the philosophical conclusion of any man, but comes directly from the Veda (Brhadaranyaka Upanishad 1.4.10 of the Yajur Veda). So it is valid, but the question is what kind of Brahman "I am".
Brahman although is one without a second, depending upon activities it is known as three:
So one Brahman is that which is enjoyed, i.e. material things of prakruti (bhogya), the second is that which enjoys (bhokta) and the third is that who gives rise to both the enjoyed and the enjoyer (prerataram). So we are Brahma, but the bhokta Brahman (the second type) and we are under the influence of Maya. But the creator Brahamn is the lord of maya.
Since, maya is the covering that is between us and God, once maya is casted out man can become Brahman. Only then the sentence I am Brahman can be fully valid. It is because maya is ignorance which prevents us from knowing and realizing Brahman. But once maya is gone, Brahma is realized. And by realizing Brahma, one becomes Brahman himself:
Now the question is, because he becomes Brahman (God), can he produce or create the other two kinds of Brahma (bhokta and bhogya)? No, he can't. Because, such a jiva who after liberation gets God, might gain other powers but creation of the world, etc. are only in the hand of Supreme Brahma. So the Brahma Sutra says:
So the identity is in the sense that the liberated jiva gets the bliss and enjoyment of equal to God. Jiva doesn't become the God. So the Brahma Sutra says:
So once, a jiva, whose consciousness has found identity with Brahma, becomes liberated enjoys the bliss of Moskhsa (emancipation) and then merges in Brahma losing all his identity. Once he has merged in Brahma, there is no coming back, there is no coming back. [BrSu - 4.4.22]
So this is generally the concept of "I am God" of the non-dualists (Advatins) who meditate upon the impersonal absolute Brahman. Identity of Brahman and jiva as one is a special realization that is attained after much practice known as Sadhana Chatushtaya (discrimination, detachment, control of mind, control of senses, meditation, etc.).
"I am God" is not a simple statement that by uttering this or knowing this one becomes God. It is a realization that has to be achieved and realized, otherwise we will only be speculating how jiva can be God, why he cannot be God etc.
I had answered the same question in another thread.
I will repeat it here again.
Hinduism does not generally believe in the concept of Creator and Creation.
While the words to this effect are told, most of the religious texts propagate this concept of "I am God".
What it means can be explained using an analogy.
If a cell in your body is analogous to one human, and the human is analogous to the universe, we can start by asking the following question....
Q : Can a cell in your body say that the HUMAN was the CREATOR, because the cell wouldn't have existed without the human, in the first place ? But interestingly enough, the human wouldn't have existed but for those cells.
So, in the same way, we can explain humanness in relation to GOD. Humans are part of the WHOLE, which we term as GOD.
So, I am God. (this must be better understood now).