The only hard dependency(without which backbone js won't work at all) is Underscore.js. Underscore is a JavaScript library that provides a whole mess of useful functional programming helpers without extending any built-in objects.
There are other dependencies required as you proceed to use more advanced features of backbone.js. For example,
Libraries for RESTful persistence(Backbone.sync)
History support via Backbone.Router
DOM manipulation with Backbone.View or Jquery