React and Flux is the hot new thing (especially the just-released React Native. Developed and used by Facebook. It is really good.
Angular (the old but popular, big thing, developed by Google). Currently between two very different major versions so I’d stay away for a few months until the dust settles.
Backbone is a good-old MVC framework for use in the client side of things.
node.js and io.js. They are the same thing, where io.js is a recent fork. Think the hudson/jenkins split. Use node.js for now, but there is a good chance that io.js will win out, so be aware.
Browserify is the best thing since sliced bread – it allows you to use npm modules in the browser, not just the server.
Gulp and Grunt are build systems. Gulp is the newer one, but pretty mature. It’s the one you should use.
express.js is what you want if you want to build stuff server-side.
Meteor is a super futuristic and cool full-stack framework that is awesome but does pretty much everything in a different way than everyone else. It’s very popular, and you should definitely try it to get your mind blown.