Base libraries (animation, dom manipulation, event handling, ajax, utility)
jQuery (this library is the most popular base library)
Zepto
Dojo
Prototype
MooTools
Utility Libraries
Underscore
Lodash
Sizzle
Modernizr (feature detection)
Yepnope (conditional loader)
MVC Frameworks
Angular
Ember
Backbone
SproutCore
ExtJS
Batman
Spine
Meteor
Exoskeleton
ActiveJS
StapesJS
JS MVC
View/Data binding frameworks
Knockout
CanJS
React
Rivets
Backbone Libraries
Thorax
Epoxy
Chaplin
Marionette
Quilt
Backpack
Rendr
Backbone Boilerplate
Templating Libraries
Handlebars
Mustache
Widget libraries (animation, ui)
jQueryUI
YUI
Bootstrap
Scriptaculous
Google Closure
ShadowboxJS
Lightbox
Mobile libraries
jQuery Mobile
Dojo Mobile
Sencha Touch
Testing Libraries
Chai
Jasmine
QUnit
Mocha
Sinon
PhantomJS
CasperJS
Istanbul
Karma
Build development Libraries
Grunt (task runner)
Bower (package manager)
RequireJS (module loader)
Yeoman (scaffolding)
Special use libraries (data-driven, graphics, maps, etc)
D3 (document manipulation)
Raphael (vector graphics)
MediaElementJS (HTML5 video/audio)
JPlayer (HTML5 video/audio)
Leaflet (maps)
ChartJS (charts)
NodeJS Libraries
Express
MongooseJS
BookshelfJS
SocketIO
Sequelize
Sails
Prerender