Now, before you begin assuming things, let me be clear: I have read all the Harry Potter books and until recently, owned all of them. I have watched every movie that has come out (up to the fifth one) so far.
I would say no, we should not be reading them. Here are a few reasons why I believe the Harry Potter books should not be read by children or even adults:
1. It gives a "glorified view of the Occult", as Mr. Baucham said in the article below. That is what all the books are about; witches, wizards, magic, tea-leaf reading, and the like. It is commonly accepted and common practice of the characters in the book. But is the Occult something to be so highly praised and tolerated? The Bible clearly teaches that sorcery and anything of that sort are an abomination to the Lord. It is referred to as "works of the flesh" in Galatians 5. We should not, willingly and unnecessarily, expose ourselves to such corruptness.
2. It gives a false view of love and romance. Harry "loves" one girl for a couple of books and then, quite suddenly, realizes that he truly loves a different girl. He ends up marrying the second girl in the last book. While some people may try to get the moral of the story and "true love", we really should examine it further. He "fell out of love" and things just sorta "stopped" with the first girl. Funny enough, those phrases and that whole concept of falling out of love is found nowhere in scripture. Romance is between husband and wife and anything different from that is not to be tolerated. As said in Titus 2 that young women are to be trained to love their husbands, not young men who they are not married to. In Proverbs 4 we are warned to keep our hearts with all vigilance for from them flow the springs of life. I know the author and books don't claim Christianity but, as Christians, we should examine what we are reading by scripture. Love is to be "patient and kind; love does not envy or boast; it is not arrogant or rude. It does not insist on its own way; it is not irritable or resentful; it does not rejoice at wrongdoing, but rejoices with the truth. Love bears all things, believes all things, hopes all things, endures all things."
3. It's a waste of time. As much as I enjoy reading (believe me, I do), why read something I know to be wrong? Especially when it's for mere entertainment purposes. It also causes your thoughts to dwell on things of this earth. We are to be dwelling on, "Whatever is true, honorable, just, pure, lovely, commendable, excellent, and worthy of praise." I have many friends whose worldviews have been shaped by books such as Harry Potter. I, myself, have had to undo and change a lot of wrong beliefs by reading fiction of that nature; I didn't realize what a change it had made on me. Now, obviously, it wasn't just these books but they definitely contributed. Even as I say this, I have heard people try to justify it by saying, "it's just a book" and "it's just fiction, it's not like it's real". It may seem to be "just a book", but people all over the world are reading it. It is popular everywhere and people love it. If it so impacts and changes our culture, then we should know and take our stance on it. It is important because everyone knows about and is affected by it. It may be fiction and not real, but it has helped change our culture. It creates a worldview of the "accepted norm"; teens expected to go through a rebellious stage, anger not kept under control, having a "crush" on several different people is ok, and so on.
So, why did I read them? Good question :). Nicole was actually the first one to read Harry Potter. I remember, us girls, sitting around her as she read some of them aloud. Those memories were always good; not because of the book but because we were gathered together, reading. I want to be like my sister in many respects and, at the time, reading Harry Potter was one of them. I must say, I enjoyed the story and the British humor made it more amusing. In that stage of our lives, books were not a huge conviction for us. The books were seemingly "clean" and fun. My discernment was very poor at that time. Over the years, our convictions have changed. My dad has taught me to examine, evaluate, and discern what I read.
For those who will try to argue that books such as these are necessary for children to be "equipped" for the culture war, I only say that I believe the Bible equips us as said in 2 Timothy 3:16-17, "All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, that the man of God may be competent, equipped for every good work."
Voddie Baucham, author of What He Must Be, wrote an insightful and thought-provoking article two years ago on the eve of the release of the last Harry Potter book. I encourage you to read it.
There are lots more reasons I could give but this gives a brief sketch on it. As Mr. Baucham says, " We need to give our children less World and more Word."