TBC by Tin - Just starting...
Library Based
Simple libraries and provides easy integration and flexibility.
jQuery - Has become the de-facto standard, but I am also looking for a commercial option for web applications.
Sencha - HTML 5 Platform with tools to visually build for mobile and desktop web applications. Buy license.
YUI - Tried before in 2010, and found it to be quite slow.
Integrated
These UI frameworks are more intrusive and require tight integration and sometimes dictate your flow.
GWT (Google Web Toolkit) - Write everything in Java and it generates the front end HTML and JavaScript.
Vaadin - Open Source, built on GWT and integrates with Spring Roo.