First, I admit that I am fairly ignorant about many of the specific claims that non-christian religions make about their god or gods. I used to be a christian and I have read more on christianity than I have any other religion so I have much more of a background in that area. So the majority of my arguments focus on that aspect of belief.
However, I have made at least some effort to know a little bit about these other religions. In all cases, the people of that religion or belief system have the burden of proof and I have not found any such proof forthcoming, nor do I find the claims to be credible on their face, and I have, in fact, found many fraudulent claims.
For example, in India there are many claims of miracles and many claims that such-and-such is a Guru who can produce vibhuti (sacred ash), who can levitate, who can produce objects from 'thin air', etc. Most often, these claims are not even allowed to be evaluated by outsiders by the guru's handlers, but when they have been tested they have been shown to be fraudulent. Most of them are not even good stage magicians. With many of them I can look at the video and SEE the slight-of-hand being used (I'm an amateur prestidigitateur myself). They aren't even trying very hard because they don't have to - the people WANT to believe and they see a miracle where I only see a scammer, a liar, and a cheat.
I do believe that people have certain types of deeply, and personally meaningful experiences as a result of either meditation or natural occurrence of these states of consciousness. However, there is absolutely no evidence that these experiences are anything other than brain states. For example, no amount of meditation has given us the mass of the Higgs particle.
Sure, these can be states conducive to creativity but nothing more than that is evidenced in thousands of years of practice.
Most christian claims of miracles are even worse. Found a job? MIRACLE! Pull some miners out of a Cave? MIRACLE! Doctor cures your cancer despite it seeming to be terminal initially? MIRACLE! Everything perceived as good is magically and automatically a MIRACLE!, no matter how much humans had to work and toil to accomplish something. And yet, nothing truly miraculous ever actually occurs - it is always within expected, normal statistical probability. This is Confirmation Bias and it does nothing to establish that some supernatural event is actually taking place.
So I dismiss these claims of miracles until something truly miraculous can be proven. You can read more in my entry But I Had A Personal Experience. If you can prove a miracle then please contact the James Randi foundation and claim your million dollar prize and THEN I will be willing to consider that your claim is valid. Until then, you can save your breath. I don't care that you found your lost dog, were cured of cancer by sneezing, survived a 30,000 foot fall, or any other ridiculous claim.
I similarly dismiss your claims that Prayer works. It's been studied (See Intercessory Prayer) and failed.
What about claims about the bible? Here are my issues with the Bible:
#1 The bible contains sections which are absolutely abhorrent to ANY sense of right and wrong and only a diseased mind can forgive them. God commands genocides and infanticides. No good god would order men to slaughter babies, period. And if you excuse this in your mind then you are sick and mentally deficient. And it undeniably does so, those people who deny the bible is commanding genocides are also clearly borderline insane.
God killing all the first-born of Egypt and god killing everyone in the flood are examples of these unimaginably abhorrent acts. The Old Testament is a tribute to a god of genocide and slavery. I cannot imagine a better book for what kind of god to REJECT than the Old Testament and the New Testament does not redeem this evil god that fails to clearly speak out against Slavery, or for equal rights for all, women are still spoken of as property and told to submit to their husbands and keep silent, and parents are told to beat their children for their own good.
Only diseased and immoral men would come up with such stories, attribute them to a god, and claim to be righteous for supporting them. The same goes for the idea of stoning people to death for things like dishonoring your Father and Mother.
#2 The bible was written 30-60 years AFTER the supposed events and there are no eye-witness accounts. Paul wasn't an eye-witness - he had a vision. The Gospel authors are anonymous and only attributed by Tradition, not by evidence of fact. For example, Luke explicitly admits he's not an eyewitness:
1 Inasmuch as many have taken in hand to set in order a narrative of those things which have been fulfilled[a] among us, 2 just as those who from the beginning were eyewitnesses and ministers of the word delivered them to us
#3 The bible has been redacted and modified and there is not a single original autograph remaining where we can verify what it originally said. Textual criticism that argues the copies we have are fairly accurate is wrong because it denies the documented fact that the early stewards of the church destroyed everything they could find that contradicted what they wished the documents to say and they murdered people who disagreed with them. You do not get to tamper with the evidence to such extremes, with 1800 years of terrorism - and then claim things were not tampered with. I do not trust them, not even one tiny bit.
The Protestant branches of this abhorrent system are no less guilty. They did not protest to the church having tortured and murdered innocent people. They protested at being held to a standard of good works for salvation -- they prefered to just claim you love Jesus and you are magically saved by faith. That's hardly a ringing endorsement for a new religious movement.
And Martin Luther, after earlier attempts to peacefully convert the Jews to Christianity, turned towards being a violent racist against Jewish peoples who wrote in Concerning the Jews and Their Lies:
That we should set fire to their synagogues and schools, and what cannot be burnt should be covered over with earth, that no man may ever discover a stone or brick of it-we are to do this for the glory of our Lord and Christianity. Burn all their houses and lodge them in stables like gypsies, in order that they may know they are not lords in this land, but in captivity and misery. Burn all their prayer-books and Talmuds, forbid the Rabbis under pain of death to give instruction, deny Jews the rights of protection on the highways, for they have no business with the land. Being neither lords, farmers not merchants, nor anything of the kind, they are to remain at home: you Lords shall not and cannot protect them, unless you would take part in their abomination. Put a flail, axe, mattock or spindle in the hands of every young and strong Jew or Jewess and compel them to do manual labor
#4 There is not a SINGLE contemporaneous historical account that would support the claims about Jesus described in the bible. The FIRST historical MENTION of Jesus appears in Testimonium Flavianum, written 60 YEARS too late and even then shows strong evidence of having been tampered with. We've no doubt that Christians existed, it is their Christ that seems to be lacking in all evidence.
But Josephus goes on at some length about Judas of Galilee - and actually attributes several events to Judas of Galilee, which are claimed of Jesus in the bible. It seems very likely that the bible authors stole those events in order to give their false Jesus some historical basis.
There are some common Myths:
#1 Myth: People wouldn't die for a false belief? Then Islam must be the truth ALSO? This myth is so blatantly wrong it's not even funny.
#2 Myth: Finely Tuned Universe - This claim is based on false assumptions and ZERO evidence. Victor Stenger (Professor of Physics and Astronomy at the University of Hawaii) ran simulations with varied physical parameters and found the claims of Fine Tuning to be false: Is The Universe Fine-Tuned For Us?
And even if Stenger's results are wrong, everyone is basing these assumptions on models that we KNOW are flawed. Quantum Mechanics and Relativity have not been unified, therefore no extrapolations can be presumed to be valid. We can propose hypotheses and test them within our present limits but without a fully validated model we CAN NOT trust such extrapolations.
I also reject the validity of Black Holes on this basis and there is a LOT of evidence for them - but it is inconclusive. We know there are super-massive objects, that is an observable fact. But we do not know that those objects are 100% accurately modeled by our present equations - we only know things seem to fit to the limit of our current ability to measure.
#3 Myth: First Cause - Again, logic alone cannot prove reality as it does not, itself, provide facts. Logical conclusions must be based on factual observations. These types of arguments are all based on pure assumptions and if Quantum Mechanics and Relativity have taught us anything about the universe it is that our classical assumptions are wrong.
So, no miracles, no prayer, no personal experiences, no bible that is trustworthy, No empirical evidence supporting any logical arguments, and evidence that the early church was bloodthirsty and violent (Inquisitions, Indulgences, Crusades, Wars, Torture, Racism, Murder, Destruction of Contrary Evidence).
There are probably a thousand other reasons I have rejected theistic claims.
Epistemically speaking, Science does not prove propositions to be true but rather demonstrates which claims are false. The problem with the god-proposition is that it cannot even be formulated in a scientifically-valid, falsifiable form - because the fact is, nobody knows a single fact about god - they only have their own wishful thinking projected onto an idea.