CiviCRM does not automatically set your members to Expired when their membership end date passes. A cron job has to be setup on your server (along with some other things) to get this to happen. Here's how to do it:
// For Drupal installs - replace <drupal_root> with the base URL of your Drupal site
$ wget 'http://<drupal_root>/sites/all/modules/civicrm/bin/UpdateMembershipRecord.php?
name=<username>&pass=<pw>&key=<sitekey>'
// For Joomla installs - replace <joomla_root> with the base URL of your Joomla! site
$ wget 'http://<joomla_root>/administrator/components/com_civicrm/civicrm/bin/UpdateMembershipRecord.php?
name=<username>&pass=<pw>&key=<sitekey>'
See the following link (green box about halfway down) for the source of these instructions. http://wiki.civicrm.org/confluence/display/CRMDOC/Membership+Types