There is no irrefutable evidence of the existence of God which could convince radical empiricists, who a priori rule out the possibility of supernatural intervention. Even if it were possible to produce video tapes of the Sinaitic Revelation, they would still say 'let us find the natural causes of this extraordinary and puzzling event.' Any recourse to supernatural causes would be categorically rejected by them. It is entirely our choice whether we want to explain the world purely in naturalistic categories and therefore treat religious faith as a phenomenon to be explained away (courtesy of Freud or Durkheim) or whether we wish to adopt a conceptual scheme, which, in addition to naturalistic modes of explanation, also is prepared to acknowledge a transcendental realm, which can be invoked for ethical and spiritual purposes. We have to realize that were we to insist on a exclusively naturalistic vocabulary, we would be utterly bereft of any guidance in the area that matters most, namely, our conduct. - Walter Wurzburger in God Is Proof Enough.
Although I take issue with Wurzburger on a number of points (on the same page he says "Since even the validity of science cannot be demonstrated, I am not uncomfortable with the fact that most thinkers agree that there is no proof for the existence of God."), but I also think that he has framed the problem succinctly: if you consider yourself an atheist or agnostic what would be sufficient proof to you for the existence of God?
Now I understand that the question begs another question: what is this God that we are trying to prove? For the sake of avoiding an even more difficult question, let's not over complicate things nor get bogged down in philosophical arguments about omniscience and omnipotence etc. and assume that we are talking about God as conceptualized by most religions: that omnipotent, omniscient, eternal entity who created the universe.
If you are up to the challenge, don't forget that you should also consider Arthur C. Clarke's Third Law: "Any sufficiently advanced technology is indistinguishable from magic." Remember, you are trying to prove God and don't want to be confused by an encounter with an extremely advanced alien life form! (So it may not help, but you still have access to any scientific instrument you desire, top scholars in any discipline, the ability to access all information gathered by humans to date.)
So let's say that you are on the level of Abraham or Moses or Balaam and can communicate with an entity that claims to be God. You want proof, however, before you are going to attempt to sacrifice your first born child (some would automatically exclude God-ness from any entity that demands this but so be it). What would you minimally require? Would you require a miracle on the level of resurrection of the dead? How about repeated and inerrant prophecy being communicated to you? A demonstration of the suspension at will of some fundamental scientific law, like the First Law of Thermodynamics?