Many people consider it an article of faith that you should capitalize every word that could possibly be related to God. Those who don't think about it much will just capitalize the personal pronouns. Occasionally it extends to adjectives (e.g. "God is a Holy God.") Sometimes adverbs, nouns referring to divine attributes, or even verbs join in the fun. For a spoof on this, see this piece at The Holy Observer.
I don't even capitalize divine pronouns, and I have very specific reasons. It's not out of lack of reverence for God. My reasons are largely biblical ones. The Bible doesn't say not to capitalize these words (though it doesn't say we should do so either). It does fail to capitalize them itself, at least in the original manuscripts (except when it capitalizes every letter). Hebrew doesn't have a distinction between capitals and lowercase, and Aramaic uses the same alphabet (I think). Greek does have the distinction, but the New Testament manuscripts are either all caps or all lowercase.
So the Bible itself doesn't capitalize divine pronouns, though some translations do. This itself creates a problem, though. What if a passage is ambiguous about whether it's referring to God or a mere human being? This isn't common, but the lack of capitalization in the original creates this possibility, and it does occur. More common in when a passage about kingship in the Old Testament refers first of all to a human king (or other type of Christ) or ideal kingship and then in an extended sense to the Messiah. Should you then capitalize the pronoun?
Some people try resolve this by not capitalizing pronouns when it's unclear but doing so when it's clear, but this makes an interpretation already, since the reader will take it as a mere human reference. Another try is to capitalize pronouns for God the Father but not for Christ, since most of the references are those fuzzy Messianic references. This creates two problems. One is the fact that some passages are hard to tell whether the references is to God or to a mere human (and some are hard to tell whether God the Father or Jesus Christ). The second problem is that this starts to make Jesus look less deserving of reverence, since the point of capitalizing was to convey reverence.
So I say we should do what the biblical authors did. We should follow ordinary capitalization conventions for our language. We should capitalize at the beginning of sentences, since that's what we do in English, and we should capitalize proper names. Other letters are lower case for the most part.
It's important to capitalize the word 'God', though. Many of my students don't do it, and it's one of my biggest pet peeves. Proper names should be capitalized no matter what sort of thing they name. I have an Ibanez guitar named Omar, an Ovation acoustic-electric named Selah, a keyboard named Vinnie, a fretless bass named Frank, and short-scale bass named Nimrod. (I guess I haven't named my djembe, my organ, or my Les Paul yet, though the latter was my brother's, and he might have had a name for it.) I once had a car named George and then one named Oscar (but no name for the current minivan). I capitalize those names.
I think students will talk about God and then think that they might not believe in him (or don't want to offend people with alternate conceptions of God), so they think somehow that means they shouldn't capitalize the name, since you don't capitalize the word 'god' when using it as a common noun. But it doesn't matter if God exists if you're using the term as a name. We capitalize the names of Spiderman, Gandalf, and James T. Kirk, even though they don't exist. So even those who don't believe in God should capitalize his name.