CB runs in a deep noConflict. The only way other jQuery can conflict is if it doesn't use noConflict, which should always be the case in a dynamic environment like Joomla. If you want to use CBs API to add jQuery you need to make the appropriate API calls as follows.
Code:
global $_CB_framework;
$js = "your jquery here";
$_CB_framework->outputCbJQuery( $js );
CBs API call handles the noConflict, namespace, and document ready. Outside of CB I can't really help you as that's entirely dependent on the implementation of the jQuery you're using.