I agree with the article on Good Nudity. I believe that when the Bible says "it was very good", what is meant is that it was created to be perfect and blameless - in other words, I believe the word "good" in the English was intended to mean so much more than it appears to be. In this respect, I believe various English versions of the Bible in common use today may perhaps be doing a disservice to the importance of the story by appearing to treat God's creation as merely "good", rather than as a true, blemish-free reflection of perfection and purity.
Adam and Eve had to cover themselves because, after eating of the tree and knowing that they had stepped out of line, they therefore couldn't handle looking at and living with the perfection inherent in the way they had been created, because they would have had to constantly deal with the fact that they were imperfect beings from that point on. Rather than becoming suicidal over the fact that they messed up, the clothing was necessary to enable them to live with themselves and at least have a chance at living life. Otherwise, I think man would have ceased to exist from that point on, because they would have just killed themselves out of grief for, and loss of, their perfect relationship to each other and the world around them, including their Creator.
God didn't need them to wear clothes, Adam and Eve needed the clothes in order to feel better about what they'd done. In addition to the reasons in the above article, I believe God gave Adam and Eve longer-lasting clothes in the form of animal skins in recognition of their free will and therefore, their choice to constantly stay covered rather than stay as God made them. After all, had they stayed unclothed, perhaps despite knowing they were imperfect, they could have learned that hiding themselves away would not have been the answer to their problems? They had a knee-jerk reaction in response to their disobedience, and clothed themselves rather than staying unclothed and therefore saying to God: "You know what? We messed up. But we know the goodness we have in us still exists, because You created us. It's going to be hard for us to constantly be reminded of what could have been (or rather, what had been), but we still would like Your help in dealing with where to go from here." Even after their initial disobedience, Adam and Eve decided by themselves to clothe themselves, not consulting God before acting. If they had talked to God about it before deciding to clothe themselves and hide, things might have been very different nowadays than they are.
Think about the metaphors - clothes are used to hide our perfectly-made bodies from each other. Lies are used to hide the truth from each other in the same way clothes are used to hide our bodies from each other. Clothes are also a metaphor for the lack of openness and truthfulness, the lack of a true relationship with each other. "I was afraid, because I was naked; and I hid myself." = "I'm lying to You, God. I know I'm lying, and I know that You know I'm lying, but I have to lie in order to hide from myself the fact that I'm lying."