'Headless Drupal' is a phrase that has been circulating around in the Drupal community for quite sometime. Basically it refers to using Drupal in a 'decoupled' sense, whereby Drupal is used in conjuction with other technologies in order to deliver an application. A common example is where Drupal is used to manage the content, but from a front-end user perspective this content isn't delivered via a Drupal theme, but is served via something like Backbone.js, Angular.js or Knockout.js.
Something to mention is that this is going to become significantly easier to achieve with the release of Drupal 8 due to the intergrated REST module.
Below is a list of resources that refer specifically to using a 'Headless Drupal' approach
Great article talking about what decoupling is, as well as explaining some of the implications and 'gotchas'.
What is Headless Drupal?
A intro into the concept of Headless Drupal, with some discussion around implementation approaches, real-life examples, pitfalls and a couple of other things
Decoupled CMS: Why "Going Headless" Is Becoming So Popular
Good page detailing what it is, why it's important, and how to use it along with various resource links.
Headless Websites: What's the big deal?
Another good intro to the topic from the folks at Pantheon.
Headless Websites - Headless Drupal Options
Looking at approaches to this in Drupal 7 & 8
Headless Drupal. Why & how a RESTful API in Drupal?
Similar to the above post, it gives an overview with some comments about achieving this in Drupal 7 & Drupal 8
Drupal Group for Headless Drupal
The group on Drupal.org dedicated to this.
Headless Drupal with Angular JS and Bootstrap
A tutorial describing how to build a very simple de-coupled Drupal web application powered by Angular JS and Bootstrap.
Building native mobile apps with Ionic & Drupal
A detailed series detailing how to go about building native mobile apps with Ionic Framework & Drupal back-end.
Came across this post after creating this list. It also gives a brief intro into the topic and lists some resource links.
Developing Drupal+AngularJS Hybrid Apps
Presentation from Drupalcamp Atlanta 2014 which walks you through the process of creating an AngularJS app combined with a Drupal module.
Decoupling Drupal Without Losing Your Head
Exploring how to avoid headless/decoupled challenges by utilising styleguide-driven development (SDD).
Making reactive Headless Drupal 8 interfaces with Meteor
Headless Drupal & Node.js | Drupal 8 RESTful
A three part series discussing how OpenLucius developed a headless system with Drupal 8, Node.js and Express.
The Future of Decoupled Drupal
A post by Drupal founder Dries Buytaert where he gives his thoughts on the subject.
Creating a RESTful API URL Alias Lookup in Drupal
Using the RESTful module with AngularJS, this post look at clean URL mapping to access data and creating a RESTful plugin for querying a table.
Decoupled CMS - Going Headless
An article discussing how the content stored in the CMS can be used in many different scenarios.