The Euthyphro dilemma -- so called, because an early version is related in Plato's dialogue between Euthyphro and Socrates -- amounts to the observation that, if we believe that some universal notion of goodness or morality is imposed on the universe by God (or by the gods, in the case of the ancient Greeks), then we seem to be forced into one of two options. On the one hand, it is possible that God chose to set up a particular morality because He knew it was the morality. God, in this picture, is generally considered to be (non-tautologically) good, conforming to the true morality precisely, and showing us right from wrong in a way that is in line with this true morality. In this picture, morality is actually separate from God, and God, being good, follows it and also enforces it to some extent.
When theists defend God on grounds that He knows better than us, and always has a good purpose in mind, they seem to be working within this first framework: God is aiming for something (objectively) good, so trust Him on that.
The other possibility is that goodness is just whatever God says it is. In that case, if God says it's right to kill babies, then it's right to kill babies. In fact, if you believe God did, as in the Bible, say to kill babies, then killing babies was at that point the right thing to do. To say that 'God is good' is pretty meaningless in this picture -- all it says is that God does what God wants God to do.
There are also 'mixture' versions. For example, some Christians say that since God made this world, God has the right to do whatever He wants with this world, and we ought to follow along with that. If we take this as referring to an objective moral statement along the lines of "if you make something, you have total control over it and it ought to obey you", then essentially these Christians are saying that there is some outside -- even potentially outside of God -- objective morality, it's just that that morality means, firstly, that we should do what God wants, and secondly, that since no-one created God, God can do whatever He wants. Frankly, I think this idea gives you the worst of both worlds and I have no idea why it is so popular.
Then there are those who say that God can do whatever He wants -- but aren't we lucky that He wants what is good for us? Such people distinguish between one sort of 'good' which is defined as 'whatever God wants', and another sort of 'good', which is defined in an almost utilitarian fashion, in terms of what makes us human beings happy and fulfilled and all the rest of it, and which God happens to like, isn't that nice? If you believe that, I guess I can understand why you praise God's goodness despite defining 'good' in terms of God -- presumably you're praising the fact that God's notion of goodness happens to coincide with your own.
I think it says something, however, that it is this coincidence with what we believe to be good that so often provides the clincher with respect to how God's goodness is viewed. It's quite rare (and, in my case, almost always nauseating) to find someone who embraces the second option of the Euthyphro dilemma without pause, excusing any and every aspect of the 'Problem of Evil' with the idea that morality is just whatever God says it is. A tsunami killed millions of people, and orphaned a whole lot of innocent kids? That's not evil, it's good, because it's what God wanted, and good is whatever God wants. No, you don't hear that very often.
I'll keep my human notions of what is good, and never mind that there appears to be no God. And if I ever discover God, then yes, I'll dare to measure Him against that notion. Unlike my fellow human beings, an all-powerful God doesn't need my sympathy or my compassion, and if God causes evil in the lives of human beings, I'll dare resist and be not resigned to a universe ruled by an amoral or immoral God. I won't give up without a fight.