There is actually a bug in the 3.6 release that causes Contact-7 forms to fail to be emailed - but it only affects those hosts using the Qmail based email systems. It appears that Wordpress used a few month old version of class-phpmailer.php one where a bug had been introduced for Qmail based email systems, the Authors of phpmailer.php had already issued an update for the file but WordPress issued the 3.6 upgrade with class-phpmailer.php version 3.5.4 (version 3.5.5 had already been fixed). In any event they are now aware of the issue and have already indicated that a more current version of class-phpmailer.php (one that is fixed for Qmail) will be included when WordPress 3.7 is released.
Meanwhile, If you go to this link:
https://github.com/PHPMailer/PHPMailer/blob/master/class.phpmailer.php
And copy the actual file contents starting with:
<?php
/*~ class.phpmailer.php
Then replace the contents of your wp-includes/class-phpmailer.php with the code from the above file, that should correct the issue if related to the Qmail bug. NOTICE!!! the name of the file is class(dash)phpmailer.php, not (dot) as it appears in the second line comment of the source.