What is the best JavaScript library?

I propose to discuss the JavaScript library on the following parameters:

• Technical and quality features : functionality, support for AJAX, etc.
  Scope of application : simple websites, blogs, web stores, etc.
  Examples of sites with a description
  Support in frameworks and CMS : Rails, CakePHP, Drupal, Joomla, etc.
  Performance : speed, code size
  Availability of additional modules , plug-ins, libraries, snippet, etc.
  Cross-browser and cross-platform
  Other options that will be interesting to discuss
  
  
  

  Libraries for discussion (links to Wikipedia)

  
  
  • Dojo
    Ext
    jQuery
    MooTools
    Prototype
    Yahoo! UI Library
    Script.aculo.us
    Other libraries
    Own library