KnockoutJS: KnockoutJS is one of the best things that can happen to a web developer. Starting to learn KnockoutJS gives you the equivalent feeling which you would feel at the very moment when you find a cup of hot chocolate in a freezing cold day. It enables your to have two way data-binding between your DOM elements and your view model which means when your data model's state changes, your UI updates automatically and vice versa. Check out its well-arranged documents and live tutorials.
Sammy.js: Last library I am considering for my every web application is Sammy.js. It gives us a nice way to handle page navigations without refreshing the page at all by providing a nice routing mechanism. Especially, if you are writing a Single Page Applications (SPA), this is the library that you want inside your suite. Don’t skip to check out its intro sample.
There are for sure other great libraries out there (e.g. Moment.js, AmplifyJS, JQuery UI, Breeze) but these are the ones I am in love at the moment. Go check them out and start exploring