Access component parameters from inside own component
To access component params in component itself, I use JFactory::getApplication() like below:
$app = JFactory::getApplication();
$params = $app->getParams();
$param = $params->get('show_create_date');
To access component parameters from another component:
$content_params = JComponentHelper::getParams( 'com_content' ); $show_date = $content_params->get( 'show_create_date' );
Or even shortcut:
$show_date = JComponentHelper::getParams('com_content')->get('show_create_date');
Get module parameters from template's index.php file:
$module = JModuleHelper::getModule('mod_headlineticker');
$headLineParams = new JRegistry($module->params);
$tickercount = (int) $headLineParams['count'];
Get plugin parameters from inside a plugin
$param = $this->params->get('paramName', defaultValue);
Get plugin parameters anywhere inside Joomla
// Get plugin 'relatedarticles' of type 'content'
$plugin = JPluginHelper::getPlugin('content', 'relatedarticles');
// Check if plugin is enabled
if ($plugin)
{
    // Get plugin params
    $pluginParams = new JRegistry($plugin->params);
    $catids = $pluginParams->get('catids');
}
Access Current Menu parameters:
$app = JFactory::getApplication();
// Get active menu
$currentMenuItem = $app->getMenu()->getActive();
// Get params for active menu
$params = $currentMenuItem->params;
// Access param you want
$yourParameter = $params->get('yourParameter');
Access Menu parameters from a known Itemid:
$app = JFactory::getApplication();
// Get Itemid from URL
$input  = JFactory::getApplication()->input;
$itemId = $input->get->get('Itemid', '0', 'INT');
// Get menu from Itemid
$menuItem = $app->getMenu()->getItem($itemId);
// Get params for menuItem
$params = $menuItem->params;
// Access param you want
$yourParameter = $params->get('yourParameter');
Template parameters from inside a template
$param = $this->params->get('paramName', defaultValue);
Template parameters from outside a template
$app = JFactory::getApplication('site');
$template = $app->getTemplate(true);
$param = $template->params->get('paramName', defaultValue);