Is there some programmatic way (or maybe a browser plugin) that allows users to arbitrarily run any jQuery they want on a webpage that is currently loaded in their browser?
FireQuery is a great Firebug extension that can include jQuery for you and from there you´re able to use jQuery in your console.
"jQuerify: enables you to inject jQuery into any web page"
This uses the Google CDN, and it's HTTPs friendly, one-line, and wrapped:
(function(){var jQueryVersion="1";var a=document.createElement("script");a.src="//ajax.googleapis.com/ajax/libs/jquery/"+jQueryVersion+"/jquery.js";a.type="text/javascript";document.getElementsByTagName("head")[0].appendChild(a);})()
You can specify the version of jQuery, e.g. jQueryVersion="2.0.2"
.
All versions are listed at developers.google.com/speed/libraries/devguide.