If you like minimal frameworks, like to make your own design decisions and want to build your own framework on top of a library, backbone is great.
If you are just looking for a minimal subset of MVC because you're doing some high-concept app that doesn't fit into the standard web application paradigm, it's worth looking at backbone.
Most importantly, if you're retrofitting an existing application, backbone will be invaluable for years.
The ideas behind it are solid and relevant today and it's not a bad idea to use it. I just believe that if you are starting a web application today, for 95% of the use cases, you are better off sticking with jQuery or moving to Ember, Knockout or Angular.
That isn't to disparage any of the other libraries and frameworks, though.