I've had this problem for four years now. Let kiddos play with books (to foster their imagination and love for books) or protect the books and keep them on a high shelf (so that they don't get ruined). While the perfectionist in me screams out for the latter of these options, the mother in me usually leans towards the first, especially because I love to read and want our children to love books too.
But that leads to the inevitable problem: torn pages in books. Recently, I discovered a great solution. Well, the solution isn't really that unique, it merely involves taping the pages up. But the type of tape is the critical point. You see at some point in the past few years we acquired some Scotch brand "Silk" tape (I think it now goes by the name of gift wrap tape). It is a more expensive version of normal Scotch tape that is meant to be used on gift wrap as it is less shiny and more invisible. I think I got it on clearance somewhere because I know I wouldn't normally buy something like that (maybe it was put there when they changed the name?). And I haven't even been really using it on gift wrap that much, as I don't really care if the already clear tape is slightly visible on a present.
However. In a book, yes. I don't want the tape to be a visible distraction to the pictures. So my solution? My clearance-rack-but-normally-expensive-name-brand silk tape.
So there you have it. The best tape for repairing books. And now you know.