Harry Potter is attacked by conservative Christians mainly because (unlike the vague staff-waving in Lord of the Rings, or the powers of "the Force" in Star Wars) parts of it SPECIFICALLY name and glorify occult witchcraft and symbolism which exists here on THIS EARTH, which the church has been at war with and trying to purge from society for thousands of years.
Some Christians are particularly concerned with the fact that this is all carefully wrapped up as a candy-coated kid's story, and by its very nature, it is aquainting young minds with the terminology and practices of the real-world pagan and satanic enemies of Christianity. Furthermore, it is painting these things in a good light and teaching children it is okay to participate in these practices. And the fear is, in the future, instead of being cautious of these types of things, the child will grow into an adult with an open mind toward these practices, already indoctrinated as a child with a full vocabulary of witchcraft and wizardry.
In my opinion, a Christian parent SHOULD be concerned, not only with Harry Potter, but with anything they're allowing their child to read or watch. Do I feel J.K. Rowling is sitting behind her desk with steepled fingers talking to Satan about how she's going to corrupt the world's youth next? Absolutely not. Have I read the books and enjoyed the movies? Absolutely. Would I let my seven-year-old read it? Probably not. In my opinion, it's just too much of a spritual risk for a child, when there are plenty of other books they could and should be reading... Like, for instance, the Bible.
Or the Jedi Academy series.

Respectfully,
--InfoDroid