We’ve created some open source apps that demonstrate how to build applications on top of the REST API.
Like Grasshopper, it shows how you can use Implicit OAuth to do authentication without a server component. It also provides examples for using the API with third-party libraries like plupload for uploading media.
Sulfur allows you to upload images, view your entire media library contents, view meta data, and delete images. You can learn more about Sulfur in this previous post.
REST API Console
For an example of a more complex application (and one that we use in real life!) check out the API Console, an interactive way of building and testing API queries.