The JavaScript codebase we are using on our website is pretty well structured (outlined here if anyone's interested).
I have been looking at integrating backbone.js (or knockout.js, for some of the features) into our code -- but after closer considerations I don't think I care that much about data binding (my appliation does not do intensive client<->server data exchange, its more biased towards server->client->js data pipe), so I don't really care if I don't have dynamic data binding and syncing.
As I am not closely familiar with those libraries, I am afraid that by opting-out of using those libraries, I am missing some other vitally helpful features. Am I?
Personally I'd use backbone if I was building a full blown single-page web-app. If your website is primarily HTML, but uses JS for some minor added functionality I'd not worry about it. Backbone is good at handling client-side data models and tying changes to those to view updates.
Personally, I've used knockout and found it's reliance on data-binding in the HTML confusing. It wasn't something that worked well for me. It might be a little bit more friendly to building websites that are partially dynamic, because a lot of the logic goes right into the html view layer. You may want to listen to this recent podcast interview the creator of knockout as it may shed some light on things. http://javascriptjabber.com/
In my case, when building a big website with some dynamic elements I've stuck with the pattern of some global jQuery plugins and page specific JS. It works well enough for simple additions to specific pages.
I don't know if this question is super specific, so here's a generic answer :)