This is not meant to be a anti jQuery post. I use jQuery in website projects that are just that, websites.
Example, in XPages, Dojo is the framework every ui widget is built upon. Anything in jQuery can be done with Dojo. Why not master Dojo?
Another reason to not consider jQuery in a business application is performance. When you use jQuery, it works in the DOM. That means to get a handle to a element, it needs to search the entire DOM every single time it needs to get a handle to a element. Worse yet, it throws away its results. So for every single cell in a fancy table, jQuery needs to pass through every single cell and then every single cell in a tree grid. This can slow down your application. You may have other events through your framework that is also doing work.
Here is what you can do on your page for other browsers if you like jQuery syntax (lets say in a XPages application).
define $ = document.querySelectorALL
Here is another good article on the topic http://www.sitepoint.com/do-you-really-need-jquery/