To refute the existence of God, I must first define what I mean by God. It seems to me that God, defined in the broadest terms, is simply: the origin of all that exists. I think most theists could agree with this basic definition (with the exception of Mormons, who believe God to have evolved from a human being). It presupposes nothing of God's alleged qualities such as omnipotence, omnipresence, and omniscience. Neither do we presume any attributes to God such as personality, gender, emotions.
Having defined God as that which is the origin of existence, we naturally move to our second definition: what is existence? Again, we will go for the broadest definition possible and say that existence is anything within space-time (including space-time itself). This definition covers not only what exists at present, but all that has or ever will exist. It includes not only the physical realm of sensible phenomena, but all that is metaphysical as well; since even something as impalpable as a thought must take place within a period of time and must arise from a brain which occupies space.
Having defined our terms, we will proceed with the following arguments:
God is the origin of all that exists.
All that exists, exists within space-time.
If 1 & 2 are true, then God is the origin of space-time.
If 3 is true, God cannot be within space-time.
If 2 & 4 are true, God cannot exist.
Therefore, God does not exist. God transcends existence.
So there you have it. God is a self-refuting concept.