Wikipedia - Occam's Razor
Occam's razor is a powerful tool in the hands of scientists. It allows them to give varying levels of probability to competing theories, and keeps modern science from being overwhelmed by complex, superfluous and redundant mechanisms.
When applied to the question of whether or not there exists a god or gods, it often yields a simple answer in the minds of the scientist asking the question: No.
However, this answer is not truly in keeping with the principles of methodological naturalism. Methodological naturalism (I will refer to it as the scientific method, or SM from now on), when applied properly to any problems dictates clearly that there is no black/white distinction. There are no "Yes" or "No" answers in science, there are only "Highly probable" and "Highly improbable" answers. Even when faced with such seemingly straightforward questions as "Will an electron and a positron annihilate when collided?" the most accurate answer given is "It is highly probable", because it is impossible to determine if every single such collision will result in the annihilation of both particles. We cannot observe every such collision.
Now, many answers are so probable that a "Yes" answer can be seen as both honest and accurate. We have never observed such a collision that did not result in the annihilation of both particles. In these cases, the answer given is usually "Yes", because it takes less effort to say "Yes" than it does to explain the whole concept of the SM, and because a less assertive answer gives the impression of a less likely probability than is truly the case. Saying "Maybe" to the above question implies that we have observed such collisions without observing the annihilation of both particles, which is untrue. For this reason, we usually say "Yes" when the proper answer is "It is likely to such a degree that we have never failed to observe it."
That being said, we have changed the answer to the question of a god's existence to "It is so unlikely that we have never observed any evidence for any god's existence."
This is nominally the most scientifically accurate answer that can be given to the question, but it still doesn't quite cut it. Occam's razor is not a fundamental principle in physics, astronomy, neuroscience, etc. It is a principle of the SM, a principle by which science is conducted, not a principle by which the universe operates, and when applied to the question of the existence of a god, the most proper answer is "There is no need to invoke the existence of any god or gods in order to explain the natural universe."
This is the answer I stand by with regards to the question. I have never observed any aspect of our universe which requires that any god or gods exist. Nor have I ever been informed of such an aspect without later learning it to be a misrepresentation or misunderstanding of the actual nature of this phenomenon.
That being said, I've pointed out that I believe in god several times.
I do not find any conflict between these two positions because of some studying in the nature of religion and universally agreed upon aspects of god or the gods.
When one looks throughout the various religions of the world which include a deity, one can find many many differences. The Germanic god Wotan demanded human sacrifices, while the Roman god Jupiter demanded the sacrifice of bulls. Ba'al has been worshiped with infanticide, while the Christian god demands no such sacrifice (contrasted with the god of the old testament, who did demand sacrifices of livestock).
One thing that all the gods throughout human history have demanded of us, however, is an acknowledgment of their existence. The ancient Egyptian gods were often themselves pharaohs, known to exist, while the demands of sacrifice necessitate an acceptance of the deity to which the sacrifice is committed.
With this being said, if any god or pantheon of gods exists, it is most logical to assume that the basis of any fundamental religion would be found in the acceptance of their existence. Another aspect which is universal is that the god or gods have some plan which they wish to succeed, and which involves humanity. In the case of the Christian god, that plan is for the 'salvation' of mankind. In the case of the Norse/Germanic gods, that plan is to achieve victory in the final battle between good and evil.
Over the course of human history, our perception of religion has shifted remarkably. Early deities began with the neolithic "mother goddess", and progressed throughout the centuries until we arrive at the modern religions such as Christianity and Islam. Perhaps the most noticeable shift in paradigms that religion has undergone is the paring down of religious requirements until one arrives at the basic requirements for the two most recent major religions: belief.
(Note that while both religions make other demands upon the adherents, the question of faith is the deciding factor in almost every interpretation.)
So those who believe in the existence of a god or gods arrive at a seeming paradox: They demand we believe in them, but there is no evidence whatsoever to suggest that we should.
So what resolves this conflict? The answer lies in the most universal phenomenon that humanity has ever encountered: Logic.
The universe operates logically. Even the probabilities of quantum mechanics obey the rules of logic. If a particle has a 70% probability of appearing in a certain spot under certain conditions, then about 7 out of 10 times it will appear in that spot under those conditions. The more times you repeat this experiment, the closer the numbers get to 7 out of 10. At 100 repetitions, it may have appeared at that spot only 69 times, but at 1000 repetitions, it may appear at that spot 697 times. At 1 million repetitions, we see it appear at that spot 699,992 times. When the experiment is performed ad infinitum, we see that the 70% probability is precisely represented. This is perfectly logical.
When we apply the rules of logic to any system, we see that they fit precisely. Therefore, any considerations of the existence of a god or gods must be logical, if it is to be as valid as the knowledge imparted to us by the SM in any other question.
So we then return to the point of what this god or these gods want from us, and we see that throughout human history, the one thing all gods have in common in this regards is our belief.
This is the point at which the SM seems to digress from religious views. If god wanted us to believe in it's existence, why not give us some evidence?
Well, consider the nature of belief. It is distinct from knowledge. There is a certain value in belief that knowledge lacks. After all, if a friend of yours is a mechanic who is about to start diagnosing some difficulties with his vehicle, you have knowledge that he will succeed. Your assurances to him that success is imminent is essentially worthless. He knows he can figure out what is wrong with his vehicle. He is a mechanic, and has performed this duty many times before.
But when you have a friend who is not a mechanic, but is forced to diagnose some difficulty with her vehicle on her own, your assurances that she will succeed can have a lasting effect. Knowing you believe in her gives her confidence that she can use to help her expedite the process. It provides a reason not to give up when faced with difficulties. Your belief in her has value to her.
This analogy translates over to the question of the existence of god in a similar form. Sure knowledge in the existence of god does not have any value, while belief in it's existence does.
To illustrate this, consider a world in which the existence of the god of the bible and of Jesus' teachings is a known fact. Every year on the fifth of August, the words "I am the God of the Bible, the father of Jesus, the savior of mankind and I truly exist" appear in glowing letter written across the sky, readable by anyone, regardless of their native language or level of literacy. Scientists have theorizes about subconscious effects, mass hypnosis, plasma dynamics and numerous other phenomenon to explain it, but no natural explanation cuts it.
Archeology and history have shown that the events portrayed in the bible truly happened as they were described. Dinosaur fossils were never found, the oldest rocks date back a mere 6000 years.
As a result of this, the whole world is Christian. Every Sunday the various churches are filled to the brim with people. Every Easter the whole of mankind awakens before dawn to glorify the sacrifice of Jesus.
So when one of us fro the real world questions one of the people from this hypothetical world about their beliefs, the conversation is simple.
"Why do you believe in the teachings of Jesus?"
"Because I know for a fact that they are true."
"Have you ever considered any other religions?"
"All other religions are false, as demonstrated by rigorous scientific investigation, coupled with the teachings of Jesus, which we know to be true."
And most importantly:
"Why don't you commit sins?"
"Because I know I will go to hell if I do."
This hypothetical world seems to be a world of black and white. Homosexuality is wrong, abstinence from sex until marriage is good. But because there is universal acceptance of what is good and what is bad, there is no black. Everything is white.
The advent of complex morality and philosophy never occurred, because there was no dissent. Art is invariably religious in nature. Technology lags far behind our own because there are no wars to spur it's development. All of the world gives charitably to those in need, so there is no hunger, poverty or upper class. As a result of this, there is very little ambition, as great accomplishments net you nothing but local fame (as the lack of warfare inhibited the advent of electronic communications, and the global media).
So what value is left? The production of beautiful artworks happens not to make people happy, but to glorify god. People are good not because they want to be good, but to avoid going to hell. Technology and the sciences are seriously underrated. There is no fortune for the ambitious to aspire to, no fame either. There is no conflict through which we can test ourselves, no difficult trials by which we temper ourselves, no diversity to explore, no differences to resolve. Everyone is the same religion. Everyone has the same social standing (except maybe the clerics). Life is stale, meaningless and pointless in this hypothetical world, and since suicide is a sin, there is no escape.
What if the evidence were not so blatant? What if it were something as subtle as the discovery in the far future that each extraterrestrial sentient species has a religion which corresponds exactly to Christianity? Well, Christianity adherency would explode. Untold billions would convert (remember, these aliens are as shocked to discover this as we are), comparisons would arise between the various versions, eventually congealing into one universal religion. Other religions die out, slowly. The various denominations of Christianity die out, as their tenets are shown to be in conflict with the 'truth'. A few generations pass, and you end up with a galaxy/galactic cluster/universe which resembles the one I described earlier, albeit with better technology.
When the existence of god is knowledge, instead of belief, the nature of mankind and of god shifts from the worthy to the worthless. God is little more than a glorified nerd, playing solitaire on his computer, while mankind is little more than a glorified computer program, mindlessly performing the function that it's user set it to.
But when the existence of god is an unknown and unknowable factor, we see the world we live in. A world of strife and evil, to be sure, but also a world of ambition, accomplishment and victory. A world in which art has value, in which differences can be appreciated as well as being a source of dissent.
And so we arrive back at the initial question. Does god exist?
The answer is the one which works the best for us, and for god. "We don't know."