First, make sure the cronjob is set to the default Magento settings. It is very important that this cronjob is executed using the wget function.
If you are using Magento1.8 / 1.9 and you are 100% sure that the cron job is set correctly, you should know that you are affected by a native Magento bug.
Open and edit the cron.php file in public_html, but don't forget to back it up locally first. In this file approximately on line 47 you have the following:
$isShellDisabled = (stripos(PHP_OS, 'win') === false) ? $isShellDisabled : true;
Bellow this line, add:
$isShellDisabled = true;
Save the file. After a few minutes, the cronjob should start.