The question "Do gods exist?" is not falsifiable, and therefore cannot be meaningfully answered, as it is always possible that a god or gods exist who choose not to cause any kind of special influence on our lives (or afterlives), even though they could if they wanted to. Though it's a moot point anyway, since such gods would also not respond in any way to worship or blaspheme, so any religious activity involving such gods would be meaningless.
The question that should really be asked is "Do gods exist who directly influence human behaviour or manipulate the universe in ways inconsistent with the laws of physics, and who use these powers to reward worshippers and punish blasphemers?", and the answer, based on currently available evidence, is no.
Certain specific gods (not mentioning any names) can be proven to not exist by a priori arguments alone. For example, an omniscient, omnipotent, and benevolent god would, by those respective properties, simultaneously know about evil, be capable of eradicating evil, and desire to eradicate evil; and therefore any universe in which evil exists is, by definition, a universe in which that god does not inhabit. Any argument that such a god allows evil to exist must concede that this god is either ignorant of evil, incapable of eradicating evil, or (worst of all from a moral standpoint) is malevolent and actually wants evil to exist.