Should pronouns referring to God be capitalized? (For example: "God will do whatever He wants.") No. There's your quick and easy answer from a real life English professor: me.
But maybe you want to know why. First, it's ugly. That should be enough.
But there's more. Let's take a look at some examples. Let's say you're a religious person writing about God. You write something like the example above: "God will do whatever He wants." My thought as a reader is stop preaching to me. Rather than getting across whatever message you're trying to get across, you're simply condescending to me, invoking some capitalization trickery to show me that your point is valid and mine isn't because your God is Big.
Let's say you're a religious person writing about God and you write the same example, but without the capitalization: "God will do whatever he wants." A reader will be more willing to read more from this person. No disrespect has been shown to God or to the reader.
Let's also imagine that you're a non-religious person writing about God. "God will do whatever He wants." The condescension of the religious person has become the mockery of the non-religious person. The "He" may as well be in quotation marks as the mocker prances around the room. In both situations, using non-caps allows people to write to each other in a civilized manner.
More important, you can write in a more objective manner. I consistently (well, when I have time for proofreading) correct my student's papers when they summon the capital pronoun. "God placed a rainbow in the sky to show that He will remember His promise." Is there anything less academic? I've never seen anyone do it for Zeus. "Zeus transformed into a swan so He could have sex with Leda." In an academic situation, the capital pronoun tells us too much about your personal life and takes away your credibility as a dispassionate critic.
C.S. Lewis argued that you should use capital pronouns for God based on the idea that it's a nice little grammar convention that prevents confusion (i.e. that you will be certain what the pronoun is referring to). But C.S. Lewis was a man who always employed what seemed like good common sense simply in order to get what he wanted (God love him).
He, like others, wanted to show "respect." Seems an odd way to show it, but I do understand the impulse. I suppose, then, that this kind of capitalization is allowed (reluctantly) in one situation: a religious person writing to an audience of religious people. But even in that case, you should know that what you are doing is "preaching to the choir." You're saying "Isn't God great?" and your readers are saying "Surely He is" and you're saying "Kind of comes across as an empty religious cliché, doesn't it?" and they're saying, "Yes, but don't it make us feel good!" Et cetera.
So there you have it. If you want ugly, condescending (or mocking) sentences that discredit your arguments and makes your words seem hollow, go ahead and capitalize. But don't be surprised when Zeus strikes you down with His thunderbolt.
BONUS GRAMMAR (in case you didn't know): Capitalize the word god only when it is used as a proper name: "Our god is named God."