Narnia- has a type of Christ, Aslan, who creates the world and sustains it. I've read the books nearly 30 times, and every time I find more and more scripture. Not sure about all the Roman and Greek mythology, but coming from a medieval literature professor, it does not surprise me.
LOTR - one of the most well written stories on the planet earth, fiction category. The hero is an example to us all - to obey God and his will in the face of the most overwhelming odds, and in the face of Satan's growing power in a world that chooses to ignore him. Anyone who has not read this series has missed one of the best fiction series on the earth.
Harry Potter - good versus evil. I do take issue with that, because the darkness has already been overcome. I just re-read this series, and enjoyed it immensely. There are lots of Christian references, since it takes place in Britain although the story itself is not necessarily allegorical to Christ.
Can these books do harm to young children or teens? My thought is the parents need to be pro-active, explain the meanings, symbolism. Childhood is an important time for the imagination to flourish. At least there is no swearing, or nudity in any of the above three. At least their purpose is not to corrupt people, but rather to get people to think about good and evil, in a metaphorical sense.
My daughter was raised on Narnia and Harry Potter. She is a strong Christian, helps people for a living, and is kind and loving. I guess these books didn't lead her down the garden path to perdition.