The reason beliefs are important to me (and should be to absolutely everybody) is that when it comes down to the nitty-gritty, all of our actions are driven by our beliefs. I keep my car on the right side of the road because I believe that oncoming traffic will do the same; I just gulped down a glass of milk because I believe that it has been pasteurized and that the date on the jug is accurate; I work to create software and hardware to test cellular phone components using a test platform that I believe is reliable and repeatable because I believe I will receive a paycheck that won't bounce; I don't jump from very high places because I believe that the speed at which I hit the ground will increase as a function of the distance I fall; I try to act kindly and with justice towards my fellow humans and other living creatures because I believe this is what makes the world a better place for all of us; you get the idea. There are also many things that I do not believe: the moon is made of cheese; the earth is less than 10,000 years old; animals can safely consume anti-freeze; putting a loaded gun into the hands of an irresponsible person is a good idea; you get the idea here also. All of these beliefs, along with the non-beliefs, guide my behavior in ways both general and specific; I think that all of our behaviors, and in fact all of what we might call knowledge, can be looked at this way: the facts we present to ourselves (and use when we reason) are based on beliefs we hold – we believe that what we hold as facts represent the true state of the world. Now, when I survey my beliefs I see that the ones about which I am most confident, the ones upon which I am (or should be – see Shermer’s discussion of the effect of reward-level on perceived risk in The Believing Brain) generally willing to stake the most important facets of my life, are the ones for which I have the greatest amount or the strongest evidence; those having very high standing are those for which the evidence is corroborated and agreed upon, especially by those who may have disagreed with the initial premise or who suspected bad evidence or evidence that had been tampered with and who have therefore approached evidential affirmation with skepticism. Evidence vetted many times over by different actors all employing skeptical inquiry in varied ways has perhaps the greatest standing of all classes of evidence. Now if you think about it for a minute, evidence amounts to just another layer of belief, really, but it's a layer that of course depends on beliefs that have themselves been previously vetted. So you can see that the strength of a belief necessarily depends on all the beliefs (or assumptions I guess might be another word) that the belief itself presupposes. The fact that human beliefs form the foundations of human behavior is not obvious but is critical; that beliefs play such an important role in human knowledge itself is just as critical. Both of these facts point to the importance of understanding the nature of our beliefs, and also to the importance of approaching such understanding with a skeptical eye.
Now, I don't think there is a being in existence who could justify each and every held belief down to the very root. We can of course also be mistaken about the ground or assumptions behind any particular belief. However, just because perfect knowledge and complete awareness is impossible in practice does not mean that the general principle doesn't apply. When we have tension between us due to differing beliefs, our only recourse is to examine the presupposed assumptions and evaluate them with respect to the things upon which we can all agree; if we cannot agree on the immediate presuppositions, we must peel back to the next layer of presupposition, and continue this until we find common ground; only then can we gradually work our way back up the chain, examining and resolving our points of difference with respect to the things we agree (or come to agree) are foundational.
Now, you clearly have any number of beliefs that I don't share; the obverse is certainly just as true. One of the beliefs you hold that I do not is that god exists; another belief that I also do not share is that god influences your life. However, the belief that god influences your life clearly presupposes the idea that god exists; so, the belief that god influences your life is actually three beliefs: 1) god exists, 2) something outside of your knowledge or control influences your life, and 3) that influential something is in fact god. That god could still exist but not actually be the thing influencing your life or thinking in any given situation is still a distinct possibility. Another possibility is that there are multiple gods and that several of them are colluding to influence you, or that a god other than the one you assume is influencing your life. I think it obvious that we can both agree that there are things that neither of us completely understands that have influenced your decisions on many occasions; where we disagree is on the cause or nature of such influence. If you concur, then we have found our first commonly foundational belief: something is influencing your thoughts and/or behavior. I also hold this belief with respect to myself – I am certain that there are things outside the scope of my direct knowledge or control that influence me personally. The next step is to look for evidence that supports each of our contrasting claims: you claim that the (or at least, an) influence is god while I claim that the influence is most likely a product of the unconscious processes that under-gird one's awareness. It is true that the evidence for either claim is in a sense subjective – at some level investigation of the phenomena surrounding consciousness will always rely on the testimony of the subject. That does not, however, indicate that all such evidence is equal – contrasting testimonials do not by definition cancel each other out perfectly. I'm sure you have heard that there are experimental methods in psychology, psychiatry, and neurology which are designed to eliminate bias; some use misdirection, for example, so that any bias possessed by the subjects may only be interjected in a manner that is inconsequential to the study's true aims. Neurologists perform real-time scans during experimental questioning to study activity in areas of the brain that have been previously established to correlate with, for example, willful deception. These techniques are of course not perfect but they are peer-reviewed and replicated. Taken together they constitute strong evidence for a number of fascinating and revealing attributes of our personalities: our brains are active in the subconscious decision-making regions for anywhere from fractions of a second to tens of seconds before we ourselves become consciously aware of a decision; our personalities can be altered in specific, predictable, and repeatable ways by either damage to or intentional stimulation of particular areas of our brain. It has repeatedly been shown that persons can be induced to feel all of the reported occurrences that have traditionally been ascribed to supernatural influence, including out-of-body experiences; the sense of a separate, and oftentimes loving presence nearby; auditory and visual intrusions; continuity of oneself with nature or a feeling of oneness with things external to one's physical body; feelings of bliss or peace; sensations of being touched; feelings of terror; the sensation of another's presence within one's own body or mind. We know from other studies that our brains are largely driven by their pattern-recognition engines, and that those regions of the brain responsible for recognizing patterns can be exhibit hyperactivity (or the opposite) which profoundly affects our perceptions and behaviors. There are also many studies that look at belief-bias (what Shermer calls Belief-Dependent realism) which also affects our perceptions and our interpretations. I see these empirical results as evidence of a very strong type – corroborated, replicated, and often approached with skepticism (or at least employing double-blind or other methodology that suitably shields the results from any bias the investigator may have).
On the opposing side there is compelling and what I'm sure is heartfelt personal testimony. I have no doubt that those who put forth such testimony are convinced of the reality of their experiences; I also have no doubt that they have indeed experienced something strange or mysterious and that such occurrences are well worth our serious attention. As I pointed out above, though, such statements invariably entail more than one belief, and I can certainly agree with some of those beliefs while disagreeing with others. Those beliefs on which all of us can (must, really) agree are directly supported by strong forms of evidence or by causal or logical links to foundational presuppositions; those about which we disagree are in such a state either because they are not supported by the evidence, or because we cannot agree on any logical/causal connection between them and our agreed-upon foundations. If we are truly at an unbridgeable impasse on a given point then we must acknowledge that the thing about which we disagree cannot be claimed by us to be objective – it isn't knowledge in any meaningful sense. Before we resort to this, however, we are obliged to go through the exercise of examining presuppositions, if we are indeed serious about resolving our differences. This is the magic of the scientific method – any and every claim or connection of this sort is always open to question; when something is discovered that calls into question a previously assumed claim, that previous assumption is again subjected to scrutiny and possible revision based on new evidence. I know I've stated before that I am not (nor is virtually any other atheist) wedded to the absolutist claim that there is no possibility whatsoever of a god existing; it's just that there is absolutely no evidence, in any but the very weakest sense, that this is true. You cited a number of things such as testimonials of life-after-death experiences and the like, but those types of claims are problematic for a several reasons: they themselves actually entail multiple beliefs that are co-dependant and whose presuppositions are almost never brought to light; they always turn out to be suspect in some way or another when they are investigated closely (i.e. there are zero or perhaps one witnesses); they are never able to be replicated under anything close to controlled conditions; they tend to exhibit strong cultural biases.
However, even if a particular individual (or even more than one) objects to a claim, we are not thereby automatically obligated to abandon that claim's status as objective; we are obligated instead to ascertain if the claim is acknowledged by many (or any) others to be valid, and whether it is supported by evidence or logical/causal connection. If evidence contrary to an assumed position is presented, we are obligated to treat it as we do all other evidence: with skepticism. We should also not be fooled by what may initially seem like a large amount of evidence: the volume of evidence is never so important as its quality. As Stenger has noted, the plural of anecdote is not data.
In addition to the lack of supporting evidence and paucity of logical connections to foundational concepts, I would have to add that there are also many very good reasons why it makes absolutely no sense for it to be true that there exists an omniscient, omnipotent, and omnibenevolent deity who intervenes in human affairs. There is also plenty of evidence that the kind of thinking that goes along with such beliefs has deleterious effects on society and human progress in general. While I can already feel the heat of your objection rising in response to that last sentence, I fully acknowledge that there are plenty of other modes of thinking are just as (and perhaps more) damaging to humanity. If you also agree with that statement, then we should be on the same page with regard to shining a spotlight on such modes of thinking. One of the differences between us is that I feel that I should not only follow where the evidence leads, but I should also verify with at least some degree of skepticism that what I am calling evidence is the real thing. And this is where we part ways on the testimony of your personal experiences. As I said above, I don’t doubt for a minute that you have had transformative and transcendent experiences. I do doubt, however, that those experiences in any way prove the existence of anything supernatural. The ‘evidence’ as I see it is that you have had such experiences; what that evidence is evidence for is up for grabs. If you want to posit that the evidence points to the existence of something, then you are of course free to do that. I have of course also had peculiar things happen that seem to stretch the limits of coincidence, although not in the numbers that you seem to have had them happen, but for my part I have an obligation to investigate further – I feel the need, and an equally strong desire, to keep peeling back layers of understanding until I reach some kind of bedrock, or the limits of understanding. I feel that this obligation is never more true than when the thing in question is something around which one is potentially going to organize one’s life. The greater the impact on one’s life-direction, the more important it is to seek a deeper understanding. This doesn’t mean that I would (or could) coerce someone into my way of thinking or reasoning, but thankfully I live in an Age that has inherited the benefits of the Enlightenment and in a country which has sanctified freedom of thought, so I can think as I do and speak my mind as I would.
The other major topic on which we diverge is inspiration. It always seems assumed that someone like myself, who places great stock in reason and science, can have no basis for inspiration other than what is tangible and in immediate view. I see the key ingredient of inspiration as being imagination, and I guess I just assumed it was obvious that nothing I have said or written disabuses anyone of imagination's power and reach. There is no need to believe (in the strong sense that equates belief with fact) anything that is not supported sufficiently by evidence and reason in order to imagine virtually any possibility, even the most fantastic. Nor does it follow that the level of one’s intellectual discipline must be inversely proportional to one’s imagination. Nor does it mean that such persons cannot be excited to the point of action by some of those possibilities. Now if the essence of inspiration isn’t imagination plus excitement, I don’t know what you are talking about. If it were not for the imagination and enthusiasm of people like Galileo, Newton, Maxwell, Einstein, and Feynman, science would not have come very far at all. In fact, to turn this around, their inspiration would have amounted to nothing at all were it not for their intellectual rigor. And I'm sure they imagined things that they later discovered were unattainable or even ridiculous – the key would be that they first imagined what might be true then discovered if those things were in fact true – they didn't just believe things to be true. Granted, the particulars of their discoveries were different from the particulars of, for example, personal experiences, but those differences do not negate the underlying principle. Inspiration drove their inquiries but was far from the whole substance of those inquiries.
Now, I understand that the source of our inspiration isn’t always obvious – you are sitting there, drinking coffee, and a wonderful and intriguing thought pops into your head. Where did that thought come from? It could have come from a god; it could have been that the previous cup of coffee’s caffeine started kicking in and caused some idle neurons to fire inside your head; maybe it was an idea or a thought you had previously but have totally forgotten about (I know that I have had thoughts that I’ve forgotten…); in the same vein, perhaps you unconsciously noticed something two days ago that stimulated unconscious processes in your brain resulting in your wonderful thought. There are many possible explanations, but what’s important to note is that from whence it comes is a matter that can itself be investigated. What is really a mystery (and a source of inspiration) to me is, why doesn’t everyone want to know the answers to these questions too? How can anyone be happy just with the simplest possible explanation that withers under even a casual investigation?