It is possible to categorize views about deities in a variety of ways. One common procedure is to classify views about the existence of deities. This classification system categorizes view about deities as:
- theism — roughly, the belief that gods or deities exist
- atheism — roughly, an absence of belief in any gods or deities, or a belief that gods or deities do not exist at all.
- deism — the belief that a god or gods exists, but does not interact with events at the scale of human beings
- agnosticism — roughly, the belief that it is not possible to know whether gods or deities exist, or the belief that one does not know.
- Some classifications group atheism and agnosticism together under the classification of nontheism — absence of clearly identified belief in any deity.
The main subcategories of theism are:
- polytheism — roughly, the belief that multiple gods or deities exist
- monotheism — roughly, the belief that only one god exists.
This taxonomy is based on beliefs about the existence of god or gods. Other taxonomies are possible. For example, a different taxonomy is based on beliefs about the nature or characteristics (rather than the existence) of God or the gods. Examples include:
- pantheism — roughly, the belief that God and the universe are equivalent
- panentheism — roughly, the belief that the universe is part of God
- dystheism or maltheism — the belief that God is not, as is often assumed, good, but is actually evil
Other categories of belief include:
- Animism: The belief that everything is alive; that spirits are in all things, or that all things have souls.
- Monolatry: The belief that there may be more than one deity, but only one should be worshipped.
- Henotheism: The belief that there may be more than one deity, but one is supreme.
- Kathenotheism: The belief that there is more than one deity, but only one deity at a time should be worshipped. Each is supreme in turn.
Polytheism is the belief that there is more than one deity. In practice, polytheism is not just the belief that there are multiple gods; it usually includes belief in the existence of a specific pantheon of distinct deities.
Within polytheism there are hard and soft varieties.
- Hard polytheism views the gods as being distinct and separate beings; an example of this would be ancient Greek Mythology.
- Soft polytheism views the gods as being subsumed into a greater whole. Most forms of Hinduism serve as examples of soft polytheism.
Monotheism is the belief that there is only one deity. There are many forms of monotheism.
- Inclusive monotheism: The belief that there is only one deity, and that all other claimed deities are just different names for it. The Hindu denomination of Smartism is an example of inclusive monotheism.
- Exclusive monotheism: The belief that there is only one deity, and that all other claimed deities are distinct from it and false — either invented, demonic, or simply incorrect. Most Abrahamic religions, and the Hindu denomination of Vaishnavism (which regards the worship of anyone other than Vishnu as incorrect) are examples of exclusive monotheism.
- Pantheism: The view that the universe is identical to a deity.
- Panentheism: The belief that the universe is entirely contained within a deity that is greater than just the universe and beyond.
Deism is the belief in god or deity based on reason. It typically rejects supernatural events (prophecy, miracles) and divine revelation prominent in organized religion, along with holy books and revealed religions that assert the existence of such things. Instead, Deism holds that religious beliefs must be founded on human reason and observed features of the natural world, and that these sources reveal the existence of a supreme being as creator. 
Atheism, as a philosophical view, is the position that either affirms the nonexistence of gods or rejects theism. When defined more broadly, atheism is the absence of belief in deities, alternatively called nontheism.
Philosophers such as Antony Flew and Michael Martin have contrasted strong (positive) atheism with weak (negative) atheism. Strong atheism is the explicit affirmation that gods do not exist. Weak atheism includes all other forms of non-theism. According to this categorization, anyone who is not a theist is either a weak or a strong atheist. The terms weak and strong are relatively recent; however, the equivalent terms negative and positive atheism have been used in the philosophical literature and (in a slightly different sense) in Catholic apologetics. Under this demarcation of atheism, most agnostics qualify as weak atheists.
While agnosticism can be seen as a form of weak atheism, most agnostics see their view as distinct from atheism, which they may consider no more justified than theism, or requires an equal conviction. The supposed unattainability of knowledge for or against the existence of God is sometimes seen as indication that atheism requires a leap of faith. Common atheist responses to this argument include that unproven religious propositions deserve as much disbelief as all other unproven propositions, and that the unprovability of God's existence does not imply equal probability of either possibility. Scottish philosopher J. J. C. Smart even argues that "sometimes a person who is really an atheist may describe herself, even passionately, as an agnostic because of unreasonable generalised philosophical scepticism which would preclude us from saying that we know anything whatever except perhaps the truths of mathematics and formal logic." Consequently, some popular atheist authors such as Richard Dawkins prefer distinguishing theist, agnostic and atheist positions by the probability assigned to the statement "God exists".
The word "agnostic" was coined by T. H. Huxley, "Darwin's Bulldog," around 1869. Since then, the word has been used in a variety of ways, as follows.
In one sense of the word, agnosticism is the position that it is not possible to know whether gods exist. Agnosticism in this sense is an epistemological position about the limits of possible knowledge. It holds that it is not possible to determine whether gods exist. Specifically, it holds that the question of the existence of gods is beyond the scope of science — that it is a question that cannot be answered by science. This position is epistemological agnosticism or strong agnosticism.
In another, more popular sense, of the word, agnosticism is a personal position. When a person describes himself as an agnostic he usually means one of the following:
- he takes no position, pro or con, on the existence of gods.
- he has considered the question of the existence of gods, and has not yet been able to decide whether he believes in the existence of gods or not.
This position is personal agnosticism or weak agnosticism.
Starting my own words here:
It is possible to be both epistemological agnostic and atheist or theist, meaning one acknowledges that it is impossible to know for certain whether god exists or not, but one beliefs that god does exist (for the theist) or that god does not exist (for the atheist) or simply not have a belief in god (atheist or nontheist).
Now quoting from wikipedia under the topic of ignosticism .
The first definition of this word is the view that a coherent definition of "God" must be put forward before the question of the existence of God can be meaningfully discussed. If the chosen definition cannot be verified empirically, the ignostic believes that it is not coherent. In that case, the ignostic holds the noncognitivist view that the truth value of the existence of God (as there defined) is meaningless (in other words, whether it is true or false does not matter).
The second definition is synonymous with theological noncognitivism, and skips the step of first asking "what is meant by God?" before proclaiming it meaningless.
Some philosophers have seen ignosticism as a variation of agnosticism or atheism, while others have considered it to be distinct. In any case, it is a form of nontheism.
More on atheism from the wiki entry on it:
Although atheists are commonly assumed to be irreligious, some religions, such as Buddhism, have been characterized as atheistic because of their lack of belief in a personal god.
Many self-described atheists are skeptical of all supernatural beings and cite a lack of empirical evidence for the existence of deities. Others argue for atheism on philosophical, social or historical grounds. Although many self-described atheists tend toward secular philosophies such as humanism and naturalism, there is no one ideology or set of behaviors to which all atheists adhere.
Humanism (from wiki entry):
Humanism is a broad category of ethical philosophies that affirm the dignity and worth of all people, based on the ability to determine right and wrong by appeal to universal human qualities—particularly rationality. It is a component of a variety of more specific philosophical systems, and is incorporated into several religious schools of thought. Humanism entails a commitment to the search for truth and morality through human means in support of human interests. In focusing on the capacity for self-determination, humanism rejects the validity of transcendental justifications, such as a dependence on faith, the supernatural, or divinely revealed texts. Humanists endorse universal morality based on the commonality of the human condition, suggesting that solutions to human social and cultural problems cannot be parochial.
Naturalism is the understanding that there is a single, natural world as shown by science, and that we are completely included in it. Naturalism holds that everything we are and do is connected to the rest of the world and derived from conditions that precede us and surround us. Each of us is an unfolding natural process, and every aspect of that process is caused, and is a cause itself. So we are fully caused creatures, and seeing just how we are caused gives us power and control, while encouraging compassion and humility. By understanding consciousness, choice, and even our highest capacities as materially based, naturalism re-enchants the physical world, allowing us to be at home in the universe. Naturalism shows our full connection to the world and others, it leads to an ethics of compassion, and it gives us far greater control over our circumstances.
Spiritual Naturalism :
Although naturalism may at first seem an unlikely basis for spirituality, a naturalistic vision of ourselves and the world can inspire and inform spiritual experience. Naturalism understands such experience as psychological states constituted by the activity of our brains, but this doesn't lessen the appeal of such experience, or render it less profound. Appreciating the fact of our complete inclusion in nature can generate feelings of connection and meaning that rival those offered by traditional religions, and those feelings reflect the empirical reality of our being at home in the cosmos.
I am a nontheist in that I do not have a belief in god. I am an epistemological agnostic in that I do not believe we can either prove or disprove the existence of god. I am an atheist in that I estimate the probability of the existence of any type of god existing as extremely low. I am atheist not only because I believe that there is no convincing evidence of god's existence, but because I believe there is evidence that discredits many of the things typically cited as evidence for god's existence, such as the Bible, Quran, fulfilled prophecies, answered prayers, spiritual promptings, near-death experiences, visions, etc.
I am a naturalist in that I do not believe in the supernatural and believe that we are fully part of the physical universe. I am a spiritual naturalist in that I still enjoy feeling the feelings I formerly believed came from the "Spirit" which I now believe are psychologically caused. I study the rules and conditions that govern when those feelings will be present.
But, as opposed to listing all those terms as descriptors of me, I typically just say I am atheist. When someone probes deeper, I tell them that I am a spiritual naturalist.
When I found out the LDS Church wasn't true, I felt no anger towards god. I was angry at Joseph, he was the one who lied time and again and took advantage of the virtuous and trusting. I believed at the time, that if there was a god, he could not lie, so he was not the one that gave me all of those spiritual confirmations of the truthfulness of the Church and the power of the priesthood, etc. I was mistakenly led to believe by Mormons that those experiences came from god, when they could not have if god is not a liar. That got me seriously thinking about whether all the times I thought I was communicating with god were actually instances of me talking to myself and whether all of those just-in-the-knick-of-time answers to prayers would have happened anyway and others were a result of confirmation bias. One thing was for sure, no matter where those experiences come from, I could not tell which ones were true and represented reality and which ones did not and apparently neither could any other Mormon who thought god confirmed the truth of Mormonism to them, so those spiritual experiences were unreliable as a source of information, although they still felt good. To me, trying to identify what is true through spiritual experiences makes about as much sense as trying to determine the nutritional value of a food by how good it tastes.
My atheism did come about through intense study of both apologetic and critical information mainly about the Bible, Christianity, and Judaism, but then about god in general as a Creator or beneficient power, and near-death-experiences, and the psychology of religion, etc. And that is why I think my atheism sticks. I don't second guess myself because I can point at the exact evidence and arguments that convince me that the probability of a god existing is extremely low, and the probability of specific gods existing such as the Jewish god is even lower than that.
It is unfair to say that atheists do not see or acknowledge the events and evidence and arguments that can and have been used to support the idea that god exists. I certainly have and do, and I have my ways of incorporating all of that into my naturalistic (god empty) worldview. I don't understand why god is the default explanation when individuals encounter phenomenon that they do not have an explanation for. For one, the concept of god doesn't explain the unexplainable as no mechanism is ever offered on how god supposedly does these miraculous feats and without a mechanism there is no explanation. It is a double-standard. We expect naturalists to offer an explanation with a mechanism (it is not sufficient to say in response to a miracle that "nature did it"), but we are somehow satisfied with the explanation "god did it". If naturalists have to provide the mechanism, then by golly, theists do too.
Two, many things that theists want to give god credit for, we already have naturalistic explanations for that they just don't know about or understand, evolution being a big one, but also many things about mental and emotional processes.
I understand that there are people who have studied Biblical criticism and still come away from it believing in Christ. There are Mormons who read all of the true history and still believe in Mormonism. I also understand that there are people who realize the natural processes, but prefer to believe that there is something godly also happening behind the scenes. To me that seems unnecessary and most likely false, but to each his or her own. I disagree, but I can see the perspective that they are taking. I acknowledge the evidence on both sides, but I believe the naturalistic perspective has the better potential of explaining both sets of evidence than the theistic perspective, especially with the many pieces of evidence that show that which we used to trust came from god does not.
We can't falsify every experience, but we have demonstrated that enough of religion is false to make me be very skeptical of that which is unaccessible for testing. And the naturalistic model has explained many things which were previously a mystery and continues to do so, so judging by previous performance, I think the naturalistic perspective is much closer to reality than the theistic one, and in any case much more useful and predictable.
I find that far too many people are too inexperienced with spiritual things or too uninformed about science and the history of religion to form an informed opinion on the matter. Personally, I think you can come to what I believe is the "right" conclusion about the likelihood of a god without having spiritual experiences, but I think you would be handicapped as you would never really know what those who have had those experiences are talking about or how you might feel about the subject if you could experience them, too.
Mormons seem to think that "you" would believe if you had only had the types of experiences they have had. Well, I have had them and I don't believe in Mormonism because I now look at those experiences differently; I no longer take it for granted that they came from god. The physical evidence, especially surrounding the Book of Abraham conclusively demonstrates that the truth and what Joseph claimed are miles apart.
Similarly, theists often seem to think that atheists would believe in god if only they had those special experiences in which you feel like you are conversing with god and that he cherishes you, or other such experiences. Well, I have had those experiences and I don't believe. And then there are ex-Mormons and atheists alike who claim believers would quit believing if them just knew the real history of their respective religions. Well, there are a number of believers who have looked at the evidence and found some way to believe.