In certain respects, classic literature, more than anything else, tends to involve those books that have endured across generations. Keep in mind, the vast majority of literature tends to be forgotten rather quickly, and this applies to works written hundreds of years ago as much as it does to works produced in the present age. That the story of Pinocchio has survived as long as it has while remaining a landmark of children's literature is itself a testament to its status as a classic.
Even so, I would note that the story is a remarkably imaginative one, one that adopts a wide range of tonal shifts, able to switch from humorous to ironic to positively nightmarish in its imagery and content. Indeed, like many of the famous children's stories (and the old fairy tales of the Brothers Grimm), this story can get very dark at times: see, for example, the character of the Coachman, or the scene where Pinocchio is hanged off a tree.
At the same time, it features a great many side characters, with well-established and memorable personalities of their own, as it follows Pinocchio across a wide array of adventures and encounters. This is a highly creative work, but it is also a work that never loses sight of its purpose and the message it wishes to impart on its readers. In many respects, it is a product of the time and culture that produced it, but there is a reason that it has endured for so very long and remains one of the most famous and influential works in all of children's literature.