jQuery - old, but still used a lot
Angular - the power of Google
Another popular framework is Angular. Angular (or AngularJS) is a structural framework for dynamic web apps. It lets you use HTML as your template language and lets you extend HTML’s syntax to express your application’s components clearly and succinctly. AngularJS’s data binding and dependency injection eliminate much of the code you would otherwise have to write. And it all happens within the browser, making it an ideal partner with any server technology.
React - virtual DOM and Facebook
VueJS - community favorite
Another excellent framework is VueJS. VueJS is a progressive framework that focuses on building user interfaces. It features an incrementally adoptable architecture that allows you to scale from simple prototypes to complex applications with ease. Vue also provides reactive data binding and composable view components for modern web development practices making it easy for developers to pick up and use in existing projects.
MeteorJS - a dark horse