React is the "View", so you need something like Backbone to fuel it. Roll your own, use Backbone, Flux (made by FB especially for React) or Reflux (third party. Flux re-imagined).
I would advise against using Backbone with React/Flux. First, because you don't need it, and secondly, because Backbone is mutable by default, which can cause all sorts of data flow bugs.
Once you buy into the Flux methodology (not necessarily Flux as described by Facebook), a lot of the concerns that Backbone handles melt away. You don't need observable collections and models because all state changes are explicit and data moves in just one direction. Given that Backbone's core is just a thin layer on top of XMLHTTPRequest, you're better off just doing XHR yourself, with POD objects for data.
Once you buy into the Flux methodology (not necessarily Flux as described by Facebook), a lot of the concerns that Backbone handles melt away. You don't need observable collections and models because all state changes are explicit and data moves in just one direction. Given that Backbone's core is just a thin layer on top of XMLHTTPRequest, you're better off just doing XHR yourself, with POD objects for data.