In my ethics class divine command theory went the way of ethical relativism. There was some squirming from the students as God was removed from the grounds of ethics. Actually, I respect DC theory more than relativism, despite my atheism, because at least it’s a theory with some philosophically interesting aspects, and not simply a confusion of the descriptive and the normative. The problem with it is that you cannot base moral principles on a stipulation, no matter who the stipulating authority might be. That would make morality entirely arbitrary—as if it were like driving on the right rather than the left. God commands us to keep our promises because it is right to do so; it’s not that it’s right because he commands it (would it be right to break our promises on God’s say-so?). Socrates’ “Euthyphro argument”, that the gods love the holy because it’s holy and not because they love it—or that God commands the good because it is the good and not because he commands it—is one of the best arguments ever produced. It shows the power of clear analytical thought. What is amazing is that after over two thousand years his incontrovertible point hasn’t yet sunk in to everyone’s mind—with so many people still thinking that morality results from God’s naked will. God doesn’t create the good; he recognizes it (assuming he exists).
I think this is a common view, but also think that things are rather more complicated than this suggests. Employing the Euthyphro argument in this way requires an overly quick conflation of 'the good' with 'moral principles'. In fact, very few divine command theorists accept this conflation in practice, and no sophisticated divine theorist -- e.g., Warburton or Adams -- does in theory, either. The point that is made by someone like Warburton, for instance, is that when talking about 'moral principles' we tend to mix up three very different things: obligations, rules of moral taste, and prudential calculations. Warburton wants to say that only obligations are moral principles in the proper sense, and that the only type of obligation for which we have any adequate account are the obligations imposed by someone superior on someone subordinate. Thus on his view, God doesn't create the good, but recognizes it; but what is recognized is not morality, but a set of vague factual principles about the nature of the good that have to be converted into morality by deliberate application to practical particulars. It's all the difference between recognizing the general rightness of 'It's good to be nice to people' and your parent telling you, 'Be nice to that kid down the street even though he isn't nice to you', between recognizing that it's good to be fair in one's dealing with others and the law establishing procedures and appeals for contracts. On such a view, only when the material (the things recognized in recognizing the good) is put into form fit for actual practice (by the will of God) do we have morality.
Thus to handle divine command theory properly, Euthyphro is simply not enough. One needs something along the lines of Cockburn's response to Warburton. In essence this requires arguing that the material is already fit for actual practice. I think this can be done, but it's an argument that becomes rather tricky in places, because it requires a good account of the normativity or authority of moral principles.