Dust.js is a good option. It is better than some of the other templating frameworks because it does not constrain that the data should be in a file, or in a string, etc.
Also it is being actively maintained https://github.com/linkedin/dustjs.
Has it been successful?
Yes, I know at least LinkedIn is using it and also contributing improvements/patches, etc.
Is it easy to use?
I have tried using it and it is as easy as Mustache or Handlebars.js.
Is it sufficiently documented?
Yes http://akdubya.github.com/dustjs.
Is community support good? (only 6 questions on ST tagged 'dust.js'!)
If you are comparing Mustache or Handlebars.js, dust.js does not have as many users, but I believe if you have an issue and post it on the LinkedIn repo they would definitely respond. I will too since I'm watching it :-)
What are the pros and cons when compared to other templating tools such as Underscore's templating, Google Closure Templates, Handlebars and Mustache.
As for pros, you can check when you should consider using dust.js here https://github.com/linkedin/dustjs#readme.
As for cons, there aren't enough users for dust.js compared to popular ones like Mustache or Handlebars.js. That said, the other libraries like Google Closure suffer the same problem.
But like I mentioned before, dust.js is designed very well compared to other frameworks IMHO.
Are there any problems using it with an MV* structure framework, e.g Backbone.js (online book)?
I have not used it with other MVC frameworks, but I don't think it should be a problem at all.
Hope that helps.