Here are four core arguments against God's existence that have persisted since ancient times. Using these four arguments as an organizing principle, I present for your consideration the Four Horsemen of 1907-1937. Arthur C. Clarke (1917-2008) also deserves mention as a contemporary of these authors as well as the Four Horsemen.
The argument from evil- If the gods are real, they have a lot of explaining to do. Albert Einstein could not imagine a god that punished the objects of his creation.
Lack of empirical evidence- Discovery trumps revelation. This is the skeptical or naturalistic argument. As H.L Mencken observed, any benefit that religion might provide is not evidence that it is true.
The argument from reasonable nonbelief- If the existence of the gods were self-evident, everyone would believe. The burden of proof is on religion. As H.P. Lovecraft observed, faith is not a virtue.