All right, here are some reasons. The thing is, if you're not a fan now, it's unlikely you'll change just because everyone else is...
1) Again, the momentum thing. It's like getting addicted to your favorite TV program after 4-5 seasons. They series started off as a pretty good read for pre-teens, and have slowly evolved over the years. My nieces were the first ones to introduce me to the series. And the books are intriguing enough to get the adults as well as the kids to read them. So basically, the target demographic goes across a large age range.
2) Two, the books are "modern", in that they're relatively easy to read, they're fun, and paced well. The interplay between characters, their growth and development, their personalities, are complex and therefore interesting. By the end of the series, I wouldn't say the target reader is a young kid any more. But the series does a good job of reminding everyone that reading can be fun.
3) Themes - while JK Rowling has her weaknesses, one of her strengths is how she touches upon the human condition. Her common themes are Love, Death, Friends, Family, Sacrifice, and more, and she's quite good in not being preachy about these themes.
4) Character development - She has several times given the 'lesser characters' their chances to shine. It's probably one of my favorite things about the series.
5) She borrows gratuitously from other modern works, everything from Tolkien to Stan Lee (creator of Spiderman). So sure, it's derivative. But in a good way. She manipulates the drama in (often) obvious ways that have already been done, but she usually copies the better examples.
6) Details. Little, little details. Who would've thunk that a small meaningless little detail in the second book plays a large role in the finale? Well, obviously, now that I've mentioned it, she did. But it's an Easter Egg, for those of us who were paying attention.