You should enter the email address in the FROM header as well:
PHP Code:
$headers = 'From: mysite.com <activation@mysite.com>' . "\r\n" .
'Reply-To: activation@mysite.com' . "\r\n" .
'X-Mailer: PHP/' . phpversion();
$headers .= 'MIME-Version: 1.0' . "\n";
$headers .= 'Content-type: text/html; charset=iso-8859-1' . "\n";
$headers .= 'Content-Transfer-Encoding: 8bit'. "\n";
$headers .= 'X-Priority: 3' . "\n";
$headers .= 'X-MSMail-Priority: Normal' . "\n";
No need to add X-Mailer BTW. It doesn't do anything and I'm pretty sure PHP adds it itself too if you omit it.