Also anything by Martin Gardner, because his books are so much fun and help to spark your imagination.

At a young age one of the most important thing to develop is a habit of perseverance and not giving up when trying to solve a problem and avoiding developing areas of learned blankness. You should develop an unfaltering confidence to use your own head when trying to solve the problems. Sharpening mental capabilities and developing good mental habits and attitudes seems to be more important than learning more things (for example, the author of many AoPS books, Richard Rusczyk, thinks that it is better for kids to sharpen their minds solving olympiad problems than learn calculus), although desire to learn more, to build your own understanding, is also important. And it is not necessary that the problems are mathematical in nature. For example, if you read Richard Feynman's "Surely You're Joking, Mr. Feynman!", you would notice that as a young boy he loved to fix things and everybody brought their broken radios to him. He would then fix them, seeing it as a challenge, as a problem to solve. He had to find a way to fix it, no matter how non-obvious the problem was. I think this helped him to sharpen his mind and instilled a good habit to see interesting problems everywhere. If you have to think for yourself, you lessen the risk of developing learned blankness. Try to think for yourself, even if it takes much more time than simply finding solution on the internet. In the long run, developing good mental habits is probably the most important thing.

Also check out the Art of Problem Solving books. They've also got some interesting resources on their website.