Yes headers are a key part in your email being delivered because they transmit the information about the email itself. Where it came from, what its labeled as, ect.
These are the headers i use to get about a 95% delivery rate.
// setup headers for mail
$headers = '';
$headers .= "From: messages@yoursite.com\n";
$headers .= "Reply-To: messages@yoursite.com\n";
$headers .= "Date: " . date("r") . "\n";
$headers .= "Return-Path: messages@yoursite.com\n";
$headers .= "MIME-Version: 1.0\n";
$headers .= "Message-ID: " . date("r") . "globale@globale\n";
$headers .= "Content-Type: text/html;charset=iso-8859-1\n";
$headers .= "X-Priority: 1\n";
$headers .= "Importance: High\n";
$headers .= "X-MXMail-Priority: High\n";
$headers .= "X-Mailer: PHP Mailer 1.0\n";
Hope this helps.