jsTree is jquery plugin, that provides interactive trees. It is absolutely free, open source and distributed under the MIT license. It is easily extendable, themable and configurable, it supports HTML & JSON data sources, AJAX & async callback loading.

jsTree functions properly in either box-model (content-box or border-box), can be loaded as an AMD module, and has a built in mobile theme for responsive design, that can easily be customized. It uses jQuery's event system, so binding callbacks on various events in the tree is familiar and easy.