The word "god" is one of those that we throw around a lot, as a culture, without ever rigorously defining it. This isn't inherently a bad thing; we refuse to rigorously define practically all the nouns we use. But in the context of this kind of conversation, that lack of definition can trip us up.
Christians tend to have a very specific definition of "god," and they call it "God." I'm gonna stick with the capital-G spelling to refer to the more-or-less consistent Christian idea of the deity, which is close enough to the Jewish and Muslim ideas of the deity for purposes of discussion, and because otherwise I'll get sick of typing God/G-d/Allah.
It's a fairly easy proposition to debate the existence of God, because God is well defined for those people who believe in Him. The Christian/Jewish/Muslim God is fundamentally like us, or I guess more to the point we are held to be fundamentally like Him. God has opinions, God has likes and dislikes, God has intentions and ambitions and emotions. God can be happy or sad. Whether you hold the opinion that God created us in His image, or whether you think we invented God to be like us, the net result is the same: God is fundamentally a person.
Lots of people have trouble believing in that. I'm one of them. I don't know if I can go so far as to say I definitively don't believe in that notion, but I'm so far down the path of "I don't know" that I'm effectively a non-believer.
But when we start talking not about God but about god, I get fuzzy.
A lot of non-Christian/Jewish/Muslim/whatever belief systems postulate that multiple gods exist, and that they're all jerks, basically. From our lofty perch at the zenith of all human achievement we can look down and tsk-tsk at those belief systems, dismissing them as naive rationalizations of the fact that life is nasty, brutish and short. Crops all died? The rain god is angry. Another tribe burned our village? The war god is angry. Jaguar ate my sister? The jaguar god is … hungry. Something. Life sucks, so we conclude that there must be some malevolent, or at least mercurial, intelligence directing the myriad ways and means by which it sucks.
I call this the theology of paranoia. There are gods, and those fuckers are out to get us.
Personally? I find this philosophy a lot easier to buy into than the notion of a parental deity who loves all of us dearly but who lets that malaria thing have a pass anyway and who takes an inappropriate level of interest in just how much time I spend soaping up my privates in the shower.
Sure, we can get all reductionist on this shit. We can study hard and learn all about how climate works and come up with metaphors based on imaginary Chinese butterflies, but at the end of the day, it still all boils down to "dammit, sometimes it just don't rain." But this is the part where Pascal's wager comes into play. If you deeply, sincerely believe that sometimes it just doesn't rain and there's nothing you can do about it, but there are those who believe there's a rain god with a hardon for animal sacrifices … is it really all that unreasonable for you to toss a goat on the bonfire once a month? Couldn't hurt, right? I mean, it's stinky, and you're out one goat, but other than that, it's an easy precaution to take. And plus, it's something to do. Life without purpose is boring.
But what if we expand our definition of "god" even further? For all their differences, the God of Abraham and the rain god with the yen for overcooked mutton still have one fundamental thing in common: They're like us. They're rational beings, entities with minds. The choices we make in life influence the deity in some way. Burn a sheep and the rain god is pleased. Masturbate and God won't answer your prayers. There's a system, and there are rules, and all we have to do to get what we want all the time is to figure out what those rules are and play by them. We can map inputs to outputs in a way that makes logical sense to us, even if, like the rules governing what is and what isn't kosher, seems pretty arbitrary sometimes.
But what if god isn't like that? What if there is a god — some kind of entity that causes things to happen somehow — and it has a mind, but its mind works in ways that are so different from ours as to be totally incomprehensible? You sacrificed a sheep yesterday, and it rained. You sacrifice a sheep again today and it doesn't rain. Why? Because yesterday your sacrifice pleased god, and today it didn't. There's no simple, linear relationship between what you do and how god reacts, because god isn't like us.
Of course … how would that be different from there being no god at all? Maybe on a practical level it wouldn't. But it would remain the case that there is a deity out there, making the sun come up and the rain fall and the jaguars eat our sisters. There's just nothing we can do about it.
What if god exists, but it actively hates us?
What if god is an animal?
What if god is a plant?
It comes down to this: It's a fairly straightforward problem to subject Christianity, or any other organized belief system, to a sort of informal scientific method. Line up a set of if-then propositions and look for the fallacy. It's not a perfect test, obviously, because belief systems are mazes of twisty little passages, all alike. But it's possible, in the broad strokes, to say that "If what you believed is true, then this would be the case, only it's not, so you're wrong."
But even if your reasoning is both applicable and correct, the very best you've done is to invalidate that one belief system. You've convinced yourself that God, as defined by thus-and-such set of beliefs, cannot exist. You haven't convinced yourself that god cannot exist, any more than you've convinced yourself that all men are Socrates.
Your question, Dorkman, was what do we believe and why do we believe it.
I believe in awe. I believe the universe is a bigger, more wondrous place than the human mind will ever be able to comprehend. I believe that in my best moments, just before sunrise, when everything is quiet and still, I can occasionally catch a glimpse of the vastness and the beauty of the universe out of the corner of my mind's eye, not enough to understand it, but just enough to be aware that it's there.
I believe that certain truths are absolute. I believe it's impossible to construct a universe in which parallel lines in a plane never intersect and yet the ratio of a circle's circumference to its diameter is equal to something other than pi. I believe that we have, through our reason and our imagination, discovered certain inviolable facts … and I believe this makes me sad. Because I believe I prefer to imagine infinite possibility than definitive, easily comprehensible truth.
But more than anything I believe that if the Christian God exists — or the Jewish one, or the Muslim one — I'll be intensely disappointed. Because I want to believe that there's more. I want to believe in the ineffable, in the infinite, in the incomprehensible. And if this whole thing, the whole entirety of existence, was thought up by an omniscient, omnipotent deity who, deep down, really isn't very different from me … sigh. That just seems like a waste of a perfectly good premise.
I want there to be a god. And I want that god to be a rhododendron a trillion trillion light-years across. And I don't ever, even in the fullness of deep time, want to understand it.