Whilst **this may not be a good idea if you don't have infrastructure to keep on top of upgrades & security issues**, the setting can be found in:

> **Administer > System Settings > Misc**.

the notifications are set in the dababase in the civicrm_setting table (along with lots of other useful little settings :))

From the "name" column, we can ascertain that:

    global $civicrm_setting;
    // Disable new version messages
    $civicrm_setting['CiviCRM Preferences']['versionAlert'] = 0;
    // Disable Security Messages
    $civicrm_setting['CiviCRM Preferences']['securityUpdateAlert'] = 0;

will disable all of the notifications.

**See Chris' answer - it's important to have the infrastructure to take care of upgrades!**