What can we know, if anything, about God by "natural theology"? That is, how much can we know about God without revelation? To put it another way, what is available to us via general revelation, not special revelation?

I think we can know quite a bit about God via general revelation. I'll base the following comments on three assumptions:
1) God exists.
2) God is much greater, in all respects, perhaps infinitely greater, than we are.
3) God created the universe.
To clarify point #2, when we describe God we are, as finite, limited creatures, seeing God "imperfectly as in a cloudy mirror", as Paul says (1 Corinthians 13:12). So I am not claiming to be able to know everything about God, nor even fully comprehending any particular facet perfectly, only that we are able to know certain things about God's nature, albeit imperfectly. Now strap yourself in; this post will be a little longer than usual, but I think it'll be worthwhile.

So first, I think we can say that God is creative. This follows from the fact that God created the universe. If God is the Creator, it means God must, in some sense, be creative. Part of being creative is intelligence. (A person might accidentally end up with something we'd call "creative", without any intelligence, by acting randomly, but we wouldn't deem it creative because it was not done purposefully.) So God would be intelligent, and it would be reasonable to say God would be (at least) more intelligent than any of us, or even more intelligent than all of us put together. Thus we could say God is omniscient (all-knowing).

Next, I think we can also say that God is omnipotent, that is, all-powerful. Not only was God creative and intelligent enough to conceive of our diverse and vast universe, but God actually acted and made it happen. Thus God has the power to do things, to make stuff happen. There is no limit to what God can do, as long as it does not contradict the other attributes God possesses. Now, God would not be limited by "time", at least not the chronological progression of events that we consider time. Since God created the universe, God would not be confined by anything within it. In this sense, then, God is outside time … God is eternal.

I'll also add that God must be, in some sense, personal. "Personal?" you may be thinking. "Why couldn't God just be an impersonal force of some kind?" One reason goes back to point #3 above. It seems a choice was made to cause our universe to exist. It wasn't something God was required to do (what would God "need"?) but chose to do. That element of choice (as well as intelligence; how can an impersonal force be intelligent?) suggests that God is, in some sense "personal", though again, in some way much more awesome than we are. McLaren is helpful here:

When people think of a person, they think of rather quaint but silly images – such as God as a Santa-esque old man … Our problem in this regard is probably a matter of words – perhaps confusing "personal" with "human". To illustrate, think of the following items: gravity, helium, water, coal, a fern, a frog, a parrot, a golden retriever, a chimpanzee, a human being … I don't know any frogs very well, but with my limited experience, they seem to have a little, but not much, in the way of personality. Parrots have more, and golden retrievers and chimpanzees more still … with each step up the ladder, we didn't lose the qualities of the previous steps; rather, we added more capabilities, more depth … while we subtracted previous limitations, going from matter to form to solidity to plant life to animal life … to human life. Let's imagine we inserted a million rungs in our ladder after human beings, each rung suggesting more developed, less limited beings, with personalities as far beyond our own as ours are beyond a bullfrog's … we'd be getting some idea of the way in which we can speak of God being personal. (Brian McLaren, Finding Faith, 129-130)

If God is not in some sense personal, in some sense relational, doesn't have something much greater than but still recognizable as personality, God would be lower than frogs, parrots and golden retrievers. That won't do. I'd say God must be, in some sense, personal.

Our list so far includes eternal, creative, all-powerful, all-knowing, and personal. What's still missing? One final thought: God is good. This is may the hardest one to accept. After all, if God is good, why do things sometimes seem so bad? But it certainly seems odd that with the trouble and strife that we see around us, every monotheistic (one-God) religion proposes that God is good. To appropriate one of C S Lewis' arguments, what would cause "primitive" man from attributing such a world to a good God if none existed?

If God is, in some sense personal, as seems to be the case from the above, how could God not be good? Caring? Loving, even? After all, if God exists, our morality, what we call good and bad, are really just terms for "Godly" and "ungodly". It's interesting to note that the Bible goes farther than calling God "good". It says that "God is love" (1 John 4:8 & 4:16).

Those are just my ideas though. We can only go so far by "general revelation" alone; eventually we must venture father into the trepid waters of "special revelation" to really know God. Why wouldn't we want to know God? Certainly a personal God could not only be known, but would want to be known, and make it possible to be known. Such a God might even go as far as coming down to our level. We couldn't comprehend God at God's own level after all. History's only person, "God in the flesh", fully God and fully human in every sense of the words, who's life (and death, and resurrection) is so compelling that today there are two billion followers around the world, is Jesus Christ. In my opinion, no other "god" compares. Check out the resources linked below, see what you think!

Further reading:

• Deep: Who is Jesus? – A five part study on Jesus' life. Fairly in-depth and information-packed.
• Shorter: Jesus: Fact or Fiction? – Interactive exploration. Many experts discuss. With videos nstuff.
• Really Short: Jesus? I Want to Know More – A brief Flash-based presentation of the "good news", the Gospel. With related links.
• As Long as you Want: Contact me