Here’s an example of the fun that can be had with an open API:
Relate-a-zon is a game you play with the Amazon catalogue in which you hop from a starting product to a target product through as few as possible intervening stepwise related products. I found it difficult and frustrating (I kept ending up in self-referential cul-de-sacs), but I can see how you can develop a skill for it. As these game hints suggest, it’s more subtle than you might first think.
They supply all the missions right now. What they ought to do is let people create and share missions. For instance, how hard would it be to get from hobbit to Babbitt? Or from humbug to Humbert?