On the wpmu.org, Harley Alexander wrote a great tutorial on turning wordpress into a mobile to-do application powered by Ajax. He used WordPress to create a simple TODO application by creating a custom theme optimized for mobile devices. You can check the Demo page (username: user, password: notes) where you can see and play with the created application, or you can download the source theme, and install it yourself.
WordPress is a good starting point because it provides a plethora of APIs for us to leverage. We’ve got Authentication, User Roles, Sanitisation, and Content Types out-of-the-box, to name a few. We don’t have to worry about admin screens. If you’re creating a complex app, you don’t even have to worry about meta boxes, taxonomies, or dealing with image upload.