Many plugin and theme developers attempt to unregister the jQuery that comes with core, and add their own copy, normally the jQuery on the Google CDN. Do not do this, it can cause compatability issues.
Instead use the copy of jQuery that comes with WordPress and aim for the version used in the latest WordPress when testing. This ensures maximum compatability across plugins.
It's tempting to modify parts of Core to remove or add things, but this must never be done. When WordPress updates, all your changes will be lost.
Instead, use Hooks/Actions and Filters to modify Core behaviour.