Backbone is mature, popular, and has both a vibrant developer community as well as a wealth of plug-in and extensions available that build upon it. It has been used to create non-trivial applications by companies such as LinkedIn.
There are no performance drawbacks to using Backbone to structure your application. It avoids run loops, two-way binding, and constant polling of your data structures for updates and tries to keep things simple where possible. That said, should you wish to go against the grain, you can of course implement such things on top of it.