When a few fellow developers that I respect started talking about Backbone.js, I liked what I heard. A few weeks later, I finally had some free time to play around with it :). After spending a mere 15 minutes thumbing through a tutorial, I already liked this framework for its sheer simplicity and reliance on existing conventions. Weighing in at under 1000 lines of code, less than 4kb minified and gzip'd, Backbone does an awful lot in a very natural way, without lots of new jargon to learn or a complicated directory structure. Backbone follows basic REST conventions, so it's easy to work it into your infrastructure if you're already following this pattern on the server side (using Rails or an equivalent MVC framework).
In addition to offering abstractions for Model and View components, Backbone also has a concept of a Controller, which is not entirely dissimilar from the one found in Rails or other MVC frameworks. Backbone's Controller, however, acts as a router and intermediary between #hash fragment-friendly URLs and your own actions and events. This means that is also has a notion of browser history baked-in (Backbone.history) which allows you to use the back button in your browser in a sane manner for navigation.
And of course, it all plays nicely with jQuery.
DocumentCloud, the organization that has open sourced Backbone, is already using it in production and will be continuing to improve upon it. Other services already using Backbone include QuietWrite, Tzigla, MapBox, and 37 Signals' Basecamp Mobile product. Although existing production deployments may not be a prerequisite to deploying a library in your own application, it certainly helps to know that others are depending on the long-term health of the code.
The Backbone.js source is hosted on GitHub. Check it out, and let me know what you think!