jQuery's primary role is to normalize the DOM API which is the one thing browsers haven't agreed on for over a decade (until IE9 came out). It's better thought of as a tool than a library. It's basically just a factory function that returns an adapter merged with a bit of decorator that wraps and normalizes the DOM object API with lots of cruft reduction and some additional goodies like the animate function and an event system that lets you fire and listen for new events on the fly on any object without even defining them somewhere first.
But I wouldn't use it as a pre-fab UI library namespace. And I wouldn't discard loops in favor of using .each on everything. And I often downshift to DOM API methods when JQuery is adding work without really eliminating cruft which brings up one of the most important features of jQuery to those of us who actually know what we're doing. It doesn't get in your way when you don't want it there.
Edit: I realize I focused on JQ a bit too much for a question that was asked more generally.
Most other popular JS tools/libraries/frameworks are either UI libraries, none of which I'm a big fan of (too inflexible typically), and rapid-application building frameworks that apply concepts from MVC or similar patterns. I'd rather DIY architecture personally (and I'm a little wary of this model-binding in templates trend) but these new frameworks aren't the sorts of things implemented by JS devs who can't handle code problems that require JS-literacy themselves I would wager.