Todos is a very simple to-do application. Users can CRUD tasks, and mark them as complete. The source is available on GitHub. [Demo]
Spine contacts is a simple address book, allowing users to CRUD contacts. The full source is available on GitHub. [Demo]
Holla is the most advanced example, and can be found on GitHub. Holla is a group chat application, and uses a combination of Rails, Juggernaut and Spine to let users chat in realtime. *WebKit only*. [Demo]
The next example shows how to easily implement infinite scrolling using Spine & Rails. The source code can be found on GitHub, and there's also a live demo.
The last example is a demonstration of integrating Spine & Rails 3. There's also an example of realtime sync in the fowa branch. [Demo]