Ember:
* Vine
* Twitch
* Square
* Heroku (dashboard)
* NBC News
* Discourse
* Huboard
* Travis CI
Backbone:
* Rdio
* Hulu
* Disqus
* Khan Academy (also uses loads of React)
* Stripe
* AirBnB
* Pandora
* Trello
etc etc..
Backbone has been around a lot longer, but Ember's apps seems to be built more recently.
Edit: Added GM.
This seems to confuse the relationship between a URL and the data displayed on the page.
I've really enjoyed React+Backbone, on the other hand. Very small footprint and gives me flexibility to design and build an application. After spending years with Rails, I've come around to "convention over configuration" is a nice thought, but breaks down at certain sizes. And it seems to break down much more quickly on the client side.
To me, personally, well-written Backbone+Underscore+React runs circles around the newer JavaScript frameworks. It's not to say the debate is over and settled - I just haven't found the complexity and size of frameworks like Ember to pay back more than they cost.
There is usually not enough emphasis on the nature of the app in these X vs Y framework discussions.
I can really see why you would choose Ember say for Discourse and why (once you got it) it is very productive.
But for other apps you might constantly fight the Framework.
Optimal patterns really depend on what you want/need to do. (Thats why TodoMVC doesn't help much).
As for the complaint about tying models to routes: Ember does want you to have a model per route, but the model can be any data structure you want: an array, a hash with multiple models, or a single model.
I'm not sure exactly what issue you hit, but most apps of any complexity have multiple models on the page, and of course that's something we support out of the box. (You can see this if you open any production Ember app in the Ember Inspector browser extension, such as http://vine.co or http://twitch.tv.)
(We're writing almost no new Backbone code these days.)
See the example/repo @ https://github.com/caseywebdev/cursors
IMO, pairing global page pub/sub with heavy local modification doesn't seem like a good pattern for effective state management. It seems less problematic at scale than two-way databinding but problematic nonetheless.
Mostly small projects and stuff. Angular definitely has a larger community, but from what I can gather on the internet Ember is used much more often as the entire basis for large applications.