While there are various proofs for God's existence, I've found this to be the simplest and therefore the most compelling. If you can refute this, let me know. Seriously, I believe this sums up the claim in Romans 1:19-20 and is undeniable. I'm sure others have expressed this argument, but here it is in my words:
For anything to exist, something must have always existed. Or to put it another way, if there was ever a point at which absolutely nothing existed, there could only be absolutely nothing now. So something exists eternally.
The physical world is decaying and will over time be completely cold and motionless, so the "eternal something" is not physical matter. If the physical world were eternal, it would have completely decayed "an eternity ago".
This "something" is self-existent, eternal, and transcends our physical/material order and is commonly and historically referred to as "God". Other names are "Prime Mover", "First Cause", "The One", etc.
To deny the existence of "God" as defined here is contrary to evidence and reason.
I recently presented this argument in this discussion on the Homeschool.com Forum . God as defined here is still a thousand miles from the God of the Bible, but this is the sure foundation that Romans 1 mentions. From here, the obvious action is for us creatures to seek out this eternal God and be thankful to Him for creating us. We should seek to know why He made us and if He has a further purpose for us. If we turn aside and worship created, non-eternal things it's obvious we are denying the Creator's special honor and should not be surprised to feel His wrath.
Romans 1:18-23
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God, or give thanks; but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools, and exchanged the glory of the incorruptible God for an image in the form of corruptible man and of birds and four-footed animals and crawling creatures.
A search for God, grounded in thankfulness and "creaturely" humility, would not be properly satisfied until it finds the mercy of God through Jesus Christ. There are surely many distractions and selfish, sinful tendencies that can thwart a search for God. It is only by His mercy and the call of His Spirit that any of us are able to find and understand the mercy He offers us.
See Exit Strategy for more on why Jesus Christ is the only proper end to any true search for the "eternally powerful divine nature" who we are all inescapably aware of.

This does not prove the
This does not prove the existence of "God". What it does is raise an age old philosophical question "can you get something from nothing?". If you answer this with "no" then it is a simplistic leap (of faith?) to the idea of a creator. But what created the creator? Does "God" have a "God" (or creator)?
This logic is simply wrong - it requires that everything had a creator and we know that this cannot be true unless something has always existed. And if you accept that something has always existed then why not accept that the universe existed without God?
God, in this case, is simply a convenient mechanism by which we explain the existence of things. We do not, however, get to explain Gods existence using this logic do we?
Nothing from Nothing
"Something does not come from nothing" is a self-evident axiom.
My argument doesn't attempt to prove "who created God", but rather shows that God is uncreated, self-existent. In the Bible, God reveals His name as "I AM" - a claim of pure eternal existence. This is another reason I believe the Bible to be the true revelation of the self-existent, inescapable divine nature. (see the Bible passage here)
We know the physical universe in which we live is not eternal since it is decaying. Current scientific understanding is that it will all burn out some day. So it can't be eternal since it would have already burned out "an eternity ago". You can speculate about oscillating dimensions of reality, parallel universes, etc. but these are mere speculations. A person can stake their eternal destiny on such speculations if they wish. However, a more reasonable, scientific approach is to realize that entropy wins in the end, therefore the self-existent God must have created all we see, and He likely has some purpose in mind for His creation.
Proving god? Not with this argument.
Incorporating Aristotle's notion of a "prime mover" into Summa Theologica and elsewhere, Thomas Aquinas famously formulated his version of the cosmological or "first cause" argument. According to this argument, the things which we see around us now are the products of a series of previous causes. But that series cannot go back in time forever. Thus there must be some first cause which was not itself caused by anything else. And that first uncaused cause is God. The argument can be put more formally as follows:
1. Every thing has either been caused to exist by something else or else exists uncaused.
2. Not every thing has been caused to exist by something else.
3. Therefore, at least one thing is itself uncaused.
There are several problems with this argument. The most crucial objection to the argument itself is that unless we know that premise 2 is true, the argument fails. If the universe is infinitely old, for instance, every thing could indeed be caused by something else before it; the series of causes could go back forever. But perhaps more importantly, one could hold that the argument succeeds without believing that God exists. There could be multiple uncaused causes--multiple gods, say--or the uncaused cause could be an unintelligent, impersonal force. Finally, the argument holds that God is required to explain the existence of the universe, but offers no explanation for why God exists. If you invoke God to answer the question "Why is there a universe rather than nothing?," you raise the further question "Why is there a God rather than nothing?" The fundamental question--"Why is there something rather than nothing?"--remains unanswered either way; so why invoke a potentially nonexistent God to explain a universe which we know exists?
eternal, powerful, self-existent
Thanks for your comment. I believe my earlier reply titled "Nothing from Nothing" addressed your concerns about "if the universe is infinitely old" and "Why is there a God rather than nothing?"
Regarding your comment "There could multiple gods ...or ... an unintelligent, impersonal force." - I agree. My point is there is something eternal, powerful, and self-existent. In this case, it seems like the logical, reasonable thing for all of us to do is to spend our short lifetimes trying to figure out what this is and if there is something required of us. Surely an eternal, powerful, and self existent Being would not create all of us for no reason at all? That's possible, but not reasonable. A self-existent, eternal being is self-sufficient and not contingent on any "creature" - so could not create out of a "need" but for some other purpose. I explore these ideas further in my Exit Strategy article.
Even if this is true...
I disagree with you about this argument's validity, but here I'm only going to address a logical fallacy in it that appears even if you accept what you have stated. Even if this premise is true, what proof do we have to accept that the Abrahamic god is this uncreated being? It could easily be someone/thing else entirely. It could be that there is an entire pantheon of deities that govern the universe, or that there is a force, not an individual being, that controls the cosmos. The logic of what you have written does not show that your god is the author of the universe; at best, it allows for any religion to assert its own story as the truth, but this poses a problem when it comes to finding anything conclusive since all of these faiths' assertions are equally valid. At the very most, the argument can make an atheist into an agnostic, but not anything else.
Christianity is the reasonable solution
As stated, the "God" of the argument is not necessarily the Abrahamic God of the Bible. However, the certainty of this "God's" existence is meant to be only the starting foundation of a search for the true creator God (or "gods" or "force" etc.) - a search which reasonable people are compelled to begin and continue until the truth is found. The truth is attainable for all who seek and the most reasonable conclusion is that Christianity is the only true religion - my reasons are stated briefly in the Exit Strategy article. Other conclusions are certainly possible, but they are not as reasonable as Christianity. Christianity's distinction is that it is the only religion in which the creature's acceptance before God is completely based on God's mercy. All other religions have some element of earned acceptance. But if God is self-existent and transcendent, how can mere creatures attain to His standard and deserve acceptance? God's infinite greatness and perfection mean that finite, imperfect creatures only gain access to Him through His mercy. Thus, Christianity in which acceptance is 100% mercy based is the only reasonable religion. I agree this is not absolute proof, but is the most reasonable solution, thus the most compelling. I develop this more in Exit Strategy.
Exit Strategy objections
I have read the exit strategy article, and I still have to say that it does not present a reason to choose the Abrahamic god over any other form of higher being/force. The article just says that one would gravitate towards the one higher being of Judaism, Christianity, and Islam because of writings of antiquity without ever explaining why. The ancient texts of the middle east do provide interesting ideas, but they are not the first to present many of these notions. In fact, if one were to compare Lao Tzu's "Tao te Ching", which was written approximately 400-500 years prior to birth of Jesus, one would encounter a myriad of similarities between to the two teachers. (I'm currently home for the holidays, so I can't provide the references right now, but give me some time and I will deliver.) With the plethora of interchangeable concepts found in many religions, including Christianity, it hard for me to see why I would choose the Abrahamic god over the multitude of gods and cosmic forces. Even the death of a divine being to save mankind from its sins is not solely the property of Christianity, as the Hindu god Krishna, the Aztec god Quetzalcoatl, and many other god can attest with their stories.
Another thing that needs to be clarified is that not all religions are concerned with the idea of creation. Buddhism, for example, considers that question unanswerable and largely ignores the issue. Also, while Buddhism is preoccupied with the afterlife, it is not the aim of the religion to get people to a favorable plane of existence. In fact, it tries to have people attain enlightenment so that when they die, they will cease to be all together. Heaven to a Buddhist is merely another realm of suffering. What I'm trying to say here is that all extant religions do not share the same views concerning their aims, so it would be specious to try to compare them in such a simplistic manner. You may try to find characteristics that are distinctive to a particular religion, but in doing so, you risk incurring the danger of overlooking extremely important aspects of other religions that give them the same level of credence as your personal faith. I just want to say that I'm not trying to be antagonistic towards you or your faith; I'm merely adding needed points to the discussion to have a richer converation.
Well-expressed thoughts
Thanks for your well-expressed thoughts. I'm out of time for tonight but will return tomorrow or Wednesday to address the points you've raised. Meanwhile, enjoy your time at home this holiday season. -Mark
Exit Strategy clarifications
Some Guy's objections (paraphrased/summarized):
"The exit strategy article does not present a reason to choose the Abrahamic god over any other form of higher being/force. The article just says that one would gravitate towards the one higher being of Judaism, Christianity, and Islam because of writings of antiquity without ever explaining why. The ancient texts of the middle east do provide interesting ideas, but they are not the first to present many of these notions..." and "not all religions are concerned with the idea of creation" and "all extant religions do not share the same views concerning their aims, so it would be specious to try to compare them in such a simplistic manner"
Exit Strategy says "The seeker would logically be anxious to consider writings of antiquity that claim to give insight to the eternal. The various scriptures of various religions seem likely candidates to be this revelation." I mean here that all ancient writings should be considered, I didn't single out those of middle eastern origin.
Now as the seeker surveys the various texts, I am proposing that the one distinction of the true religion is that "access to the divine" would be based purely on God's mercy. I mean "access to the divine" to incorporate a variety of benefits such as eternal life, divine favor in this physical life, wisdom for one's earthly lifetime, an understanding of life's origin and purpose, etc. The Proving God article focuses on creation/origins and Exit Strategy focuses on the afterlife, but these were not meant to be an exhaustive list of religious concerns. Exit Strategy does reason that obtaining a favorable existence in the afterlife should be everyone's top concern, but indeed it's not the only concern.
Regarding the distinction of mercy, I mean that everyone should be aware of their great limitations and should expect that any efforts to work toward or earn "access to the divine" will always fall short. If God (my term for "the divine") is creator, He is infinitely greater than we are and our greatest efforts will always be inadequate. Now, all religions except one describe and command a way in which humans earn God's acceptance. I claim this is a fundamental flaw and proves these religions are false. Only Christianity claims that mankind is completely helpless and that God has mercy and provides access, through Jesus, for those who have ceased their own striving and simply fall at God's feet, helpless and trusting in none of their human righteousness. This is the only reasonable way in which "access to the divine" is opened, in which the infinite chasm between God and man is bridged.
Here are a few biblical texts that describe this better. Could you take a day or two to think about what I've said here, then get back to me if you have further questions or suggestions? We have holiday activities the next few days so my online activity will be intermittent. I appreciate the tone of your earlier comments and would enjoy further conversation. -Mark
Isaiah 66:1-2 Thus says the LORD, "Heaven is My throne, and the earth is My footstool. Where then is a house you could build for Me? And where is a place that I may rest? For My hand made all these things, Thus all these things came into being," declares the LORD. "But to this one I will look, To him who is humble and contrite of spirit, and who trembles at My word."
Luke 18:9-14 And Jesus also told this parable to certain ones who trusted in themselves that they were righteous, and viewed others with contempt:
"Two men went up into the temple to pray, one a Pharisee, and the other a tax-gatherer. The Pharisee stood and was praying thus to himself, 'God, I thank Thee that I am not like other people: swindlers, unjust, adulterers, or even like this tax-gatherer. 'I fast twice a week; I pay tithes of all that I get.' But the tax-gatherer, standing some distance away, was even unwilling to lift up his eyes to heaven, but was beating his breast, saying, 'God, be merciful to me, the sinner!'"
"I tell you, this man went down to his house justified rather than the other; for everyone who exalts himself shall be humbled, but he who humbles himself shall be exalted."
Romans 9:30-10:4 What shall we say then? That Gentiles, who did not pursue righteousness, attained righteousness, even the righteousness which is by faith; but Israel, pursuing a law of righteousness, did not arrive at that law. Why? Because they did not pursue it by faith, but as though it were by works. They stumbled over the stumbling stone, just as it is written, "BEHOLD, I LAY IN ZION A STONE OF STUMBLING AND A ROCK OF OFFENSE, AND HE WHO BELIEVES IN HIM WILL NOT BE DISAPPOINTED."
Brethren, my heart's desire and my prayer to God for them (Jews) is for their salvation. For I bear them witness that they have a zeal for God, but not in accordance with knowledge. For not knowing about God's righteousness, and seeking to establish their own, they did not subject themselves to the righteousness of God. For Christ is the end of the law for righteousness to everyone who believes.
Romans 10:9-13 if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you shall be saved; for with the heart man believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. For the Scripture says, "WHOEVER BELIEVES IN HIM WILL NOT BE DISAPPOINTED." For there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call upon Him; for "WHOEVER WILL CALL UPON THE NAME OF THE LORD WILL BE SAVED."
1 Peter 1:3-5 Blessed be the God and Father of our Lord Jesus Christ, who according to His great mercy has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to obtain an inheritance which is imperishable and undefiled and will not fade away, reserved in heaven for you, who are protected by the power of God through faith for a salvation ready to be revealed in the last time.