Several JavaScript-based UI frameworks

Mochaui
Mochaui is a Web Applications User Interface library built on the mootools JavaScript framework.
URL: http://mochaui.com/
Demo: http://mochaui.com/demo/
Authorization method: MIT license

Jquery UI
URL: http://ui.jquery.com/
Demo: http://ui.jquery.com/demos
Authorization method: MIT and GPL licenses

Jquery UI Layout
URL: http://layout.jquery-dev.net/
Demo: http://layout.jquery-dev.net/demos.html
Authorization method: Dual-licensed under the GPL and MIT licenses.

Dojo
URL: http://dojotoolkit.org/
Demo: http://dojotoolkit.org/demos
Authorization method: BSD license and the academic free license

Rico
URL: http://openrico.org/
Demo: http://demos.openrico.org/
Authorization method: Apache 2.0 license

Vegui
URL: http://www.vegui.org/
Demo address: http://demo.vegui.org/
Authorization method: MIT license

Openlaszlo
If you have heard of openlaszlo before, you will surely think that it is only Flash development. However, openlaszlo now supports the development of pure JavaScript applications.
URL: http://www.openlaszlo.org/
Demo: http://www.openlaszlo.org/showcase
Authorization method: common public license (version 1.0)

Jxlib
A mootools-based UI Library
URL: http://jxlib.org/
Demo: http://jxlib.org/
Authorization method: MIT license

Qooxdoo

URL: http://qooxdoo.org/
Demo: http://qooxdoo.org/demo
Authorization method: lgpl/EPL dual license
ZK
URL: http://www.zkoss.org/
Demo address: http://www.zkoss.org/demo/
Authorization method: GPL license
Yui
Web: http://developer.yahoo.com/yui/
Demo: http://developer.yahoo.com/yui/examples/
Authorization method: BSD license
Extjs
URL: http://extjs.com/
Demo: http://extjs.com/products/extjs/
Authorization method: dual licensing model