Now in March 2016 it says 69.8% of websites use jQuery for a 96% marketshare vs a 2.9% for Prototype. Used 33.1 times more
Others include Bootstrap, Modernizr, MooTools
But another article says "Much of this growth can likely be attributed to the fact that jQuery comes bundled with a number of popular open source blogging and content management software systems, including DotNetNuke, Drupal, and WordPress. Sysadmins who are running these systems might not be aware that they are using the library." (from here)
JQuery has a mobile web framework too (from here)
A March 2011 comment (from here)-- Having used Prototype, Scriptaculous and jQuery. I find jQuery to be far more powerful, in that I tend to write far fewer lines of code than with Prototype.
I think what makes it particularly useful/powerful is:
A Dec 2009 comment -- I was working with Prototype before, and I switched to JQuery because: