It's simple & lightweight compared to the other leading JavaScript libraries/frameworks such as AngularJs, EmberJs or even ReactJs. Easy to understand and start writing the app in the same day. I use it for prototyping while test tasks at the interviews or pet projects. Backbone plays well with the other JS libraries and tools out there. Definitely, love their implementation of models/collections.

The concept of models and collections are fun to use. Initially they were a little difficult to comprehend but very powerful once mastered. Also, backbone was one of the first frameworks to introduce data binding and it's really wonderful when mixed with MongoDb for a RESTFUL application. Though there are many MV frameworks out there, Backbone is one that doesn't complicate things. I like Backbone because of the ease of use when working with jQuery plugins. Other frameworks don't recommend using jQuery with them but jQuery is one of the dependencies of Backbone. Backbone also has Marrionette which is another framework on top of Backbone, it provides more complex features like Region management and Memory management for large scale applications.

The fact that it's not very opinionated. It gives a lot of freedom to the programmer to decide what's the best architecture he wants to use. Also, the fact that the framework size is very small in terms of bytes, especially for mobile phones, that's a big plus, it loads very fast.