There are so many reasons I love the Harry Potter books- but I think the main one is that they are so carefully crafted. Since J.K. Rowling had all seven books planned out before the first one was published, she was able to sprinkle the books with details that seem small when first introduced but become extremely important later.
I absolutely love reading the books the first time- there is nothing like the thrill of having no idea where the author is heading- but it's the rereading that has made me really appreciate them.
Let me give you an example.
At the end of the sixth book... (spoiler alert- don't read past this point if you haven't finished reading Harry Potter and the Half Blood Prince yet)...
Extra space for anyone who wants to stop reading now
... there is a black cabinet that figures significantly into the plot. When Draco and Dumbledore are "conversing" on top of the astronomy tower- Dumbledore asks how Draco managed to get Death Eaters into Hogwarts. Draco replies that he "had to mend that broken Vanishing Cabinet that no one's used for years. The one Montague got lost in last year." (Half Blood Prince, page 586).
Okay, so it's easy to assume that this is the first mention of the cabinet, right? Nope- it's the FIFTH time it's mentioned. Take a look.
All page numbers refer to the hardcover Scholastic editions.
Harry is in Filch's office when he and Filch hear a huge BANG! on the floor above. Filch races out of his office (while Harry reads about the Kwikspell course.) When Filch comes back in, he says "that vanishing cabinet was extremely valuable!" (Chamber of Secrets, pg. 128)
Harry leaves Filch's office and "Nearly Headless Nick came gliding out of a classroom. Behind him, Harry could see the wreckage of a large black-and-gold cabinet that appeared to have been dropped from a great height. "I persuaded Peeves to crash it right over Filch's office," said Nick eagerly. "Thought it might distract him."(Chamber of Secrets, pg. 129)
In Book 5, Harry is upset when Draco deducts points from Gryffindor and he comments on it to Fred and George.
"Malfoy just docked us all about fifty points," said Harry furiously...
"Yeah, Montague tried to do us during break," said George.
"What do you mean, 'tried'?" said Ron quickly.
"He never managed to get all the words out," said Fred, "due to the fact that we forced him headfirst into that Vanishing Cabinet on the first floor." (Order of the Phoenix, pgs. 626-627.)
When Harry goes into the Room of Requirement in the sixth book to hide his Potions book
"he turned right past an enormous stuffed troll, ran on a short way, took a left at the broken Vanishing Cabinet in which Montague had got lost the previous year.
(Half Blood Prince, pg. 526)
Also, the cabinet in Borgin and Burkes is mentioned twice. Once in Book 2 (when Harry actually hides in it so that the Malfoys don't see him) and once in Book 6, when Harry, Ron and Hermione can't get a clear view of Draco talking to Borgin because the cabinet is in the way. I'll add the page references when I have the books in front of me.
This is just one example of how Rowling has littered clues and intriguing information throughout the series. Even if you've read the books before, I think they're always worth picking up again.