Currently I am making an online enquiry form with a set of fields that are non-mandatory.

If a non-mandatory form field is not filled-in out, I would like to make it so that it doesn't come through in the processed email.

For instance; if someone does not enter their telephone number, the "Telephone: $atelephone" component does not come through.

if ($atelephone != '') {
echo "Telephone: ".$atelephone;
}

I figure the code should have something like above put in it, though I am struggling to connect the dots. Any help would be greatly appreciated. (I hope this makes sense).

<?php 

// Base form items

$asender = $HTTP_POST_VARS['name'] ." <". $HTTP_POST_VARS['email'] .">";
$asubject = "Email Enquiry: ".$HTTP_POST_VARS['subject'];
$arecipient = "[email protected]";

/*******************************************************/
// Mail form variables //

$aname = $HTTP_POST_VARS['name'];
$aemail = $HTTP_POST_VARS['email'];
$atelephone = $HTTP_POST_VARS['telephone'];
$asuburb = $HTTP_POST_VARS['suburb'];
$aenquiry = $HTTP_POST_VARS['enquiry'];

mail("$arecipient","$asubject",
"
===========================================
Please note: this is an email
generated from the Website.
=========================================== 

Name: $aname
Email: $aemail
Telephone: $atelephone
Suburb: $asuburb

Message:
$aenquiry 

================================ ","FROM:$asender"); 

header('Location: /thank-you.php');

?>

You're on the right track. The last step is make a string to input in your final message:

$_POST['telephone'] ?
  $telephoneString = "Telephone: ".$_POST['telephone'] ."\n" :
  $telephoneString = "";

(The \n at the end of the string makes a newline.)

Then, output the string in the message. It will be empty, or not.

  "foo bar baz
  ===========================================".
  $nameString.
  $emailString.
  $telephoneString.
  $suburbString;

Edit

This may work better for individual form fields. However, for elegance, I prefer the solution from @mazzzzzz.