Sample Rails 4.1.x application for Everyday Rails Testing with RSpec: A Practical Approach to Test-driven Development by Aaron Sumner. This repository demonstrates incremental testing of an existing application, starting with an untested codebase and working through model, controller, and feature specs.
Each chapter's progress has a specific branch in this repository. See chapter 1 of the book for details.
Using Git, you can check out each version by name. See details in the book.
If you're not comfortable with Git, you can also use GitHub's handy branch/tag filter to select a specific tag and browse the source code online. To learn more about Git, I recommend the free resources Git Immersion or Try Git.