The API can be used from any application by sending basic HTTP requests; however, client libraries simplify the process of querying or creating specific resources. These libraries make it easy to connect an external application to the WordPress REST API using a variety of programming languages.
Aside from the Backbone.js client, these libraries are not part of WordPress core, and are not necessarily maintained or endorsed by the WordPress REST API team.
Requests for PHP is a general purpose HTTP request library. While not specifically designed for the WordPress REST API, it is a great tool for interacting with any HTTP API.
The Backbone.js client is built in to WordPress core and provides Backbone.js models & collections for working with REST API resources.
ember-wordpress provides a connection between Ember Data and the REST API
wp-api-client: a read-only REST API client written in Ruby.
WordPressPCL: a full REST API client written in C#.
wordpress_client: A library exposing a fluent api to interact with the WordPress REST API.