This w3techs.com current article claims 20.5 times more websites use JQuery than use Prototype. JQuery is used by 57.4% of all websites and prototype is used by 2.8%. from here. in Dec 2013
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)
From Dec 2011 "Reading the prototypejs mailing list archives, it's pretty clear that prototypejs is pretty much dead at this point in time. The tapestry5-jquery team have done a great job replacing prototypejs with jquery which is pretty much the defacto javascript library these days. "
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:
$('.tab').hide()
could hide all elements of class tab$(':input').parents(':not(:first)').show()
would show all the parents of every input element except the first parent.
A Dec 2009 comment -- I was working with Prototype before, and I switched to JQuery because: