The thing I liked about Harry Potter was that although they were fairly light, entertaining, and suitable for almost any age, they still contained elements of mature consideration. It wasn't always the main theme, but the whole series ended up being not just a fight against an ultimate evil, but showing how young kids grew up and were changed by that adversity.
A lot of young people grew up alongside the characters in the books.
Suitable for adults, and a great series for kids to read. The series is a great way to get kids involved in reading. They may even move from the HP books into more mature, adult literature. Kind of like how The Hobbit is more suitable for kids, but makes a great introduction to get you started on LOTR, which is a darker, more involved book.
Ofttimes a story is considered classic only because it was written in a different era. H. G. Wells, Lovecraft, Verne etc. were really just science pop fiction at that time. Today they are examples of great sci-fi. Maybe not "Classic Literature", but I've read some of that too, and it often doesn't seem that great once you get used to the unusual way people spoke in those days.