since $email_results is an array, $to = $email_results; should be $to = $email_results['emilids2']; since that is the column with the email address.
also, you need a { } enclosing the body of your while loop.
<?php
//connect to database
$email_search = mysql_query("SELECT * FROM emailcollection WHERE emilids2 !=''");
$message=stripslashes(trim($HTTP_POST_VARS['email_message']));
$subject=stripslashes(trim($HTTP_POST_VARS['email_subject']));
while ($email_results = mysql_fetch_array($email_search)) {
$to = $email_results['emilids2'];
mail($to, $subject, $message, "From: \"The Young Americans Project\" <your@email.com>");
}
?>