JQuery is dual licensed under the GNU General Public License and the MIT License and is hence, free and open source. This allows you to either manipulate the source or implement its range of functions in your scripts for free.
Recently, Nokia and Microsoft have announced plans to bundle JQuery on their platforms. Nokia has plans to integrate this tool on their Web Run-Time platform, while Microsoft is gearing up to provide this framework with their ASP.NET AJAX and ASP.NET MVC framework in particular and the Visual Studio environment in general.
We had a brief discussion on MooTools last week. Though JQuery and MooTools are similar tools by nature and provide the developers with almost the same set of features, however they have minor differences and are unique in their own way.
Effects and Animations can also be developed using the JQuery platform but however, I personally felt MooTools scores over JQuery in this regard. So, if you want rapid code development with standard animations and a neat look and feel, go for JQuery. If however, you are on the lookout to deliver more eye-candy animations all over your page, MooTools should be the obvious choice.