Alternatives to the massive if-else statements.

Alternative.php

<?php
function register()
{
  // Just return the form because there's no need going through the rest of the call stack below.
  if (empty($_POST)) return register_form();

  // Setting some defaults.
  $msg = '';
  $success = false;
  try
  {
    /* Rule: Place the error message close to the validation rule.
            Updating the validation rule should help you notice & update the error message. */
    if (empty($_POST['user_name']))
      throw new Exception('Empty Username');

    if (empty($_POST['user_password_new']))
      throw new Exception('Empty Password');

    if ($_POST['user_password_new'] !=== $_POST['user_password_repeat'])
      throw new Exception('Passwords do not match');

    if (strlen($_POST['user_password_new']) < 6)
      throw new Exception('Password must be at least 6 characters');

    if (strlen($_POST['user_name']) > 64 || strlen($_POST['user_name']) < 2)
      throw new Exception('Username must be between 2 and 64 characters');

    if (!preg_match('/^[a-z\d]{2,64}$/i', $_POST['user_name']))
      throw new Exception('Username must be only a-z, A-Z, 0-9');

    $user = read_user($_POST['user_name']);
    if (isset($user['user_name']))
      throw new Exception('Username already exists');

    if (empty($_POST['user_email']))
      throw new Exception('Email cannot be empty');

    if (strlen($_POST['user_email'] > 64))
      throw new Exception('Email must be less than 64 characters');

    if (filter_input(INPUT_POST, 'user_email', FILTER_VALIDATE_EMAIL) === false)
      throw new Exception('You must provide a valid email address');

    create_user();
    $success = true;
    $msg = 'You are now registered so please login'; // Update with the success message
  }
  catch (Exception $ex)
  {
    // All exceptions are handled in the same way.
    $msg = $ex->getMessage();
  }
  
  if (!empty($msg))
    $_SESSION['msg'] = $msg; // Needed for both success/failure case anyways

  if ($success)
    header('Location: '.$_SERVER['PHP_SELF']); exit(); // Just redirect
  else
    return register_form();
}

Original.php

<?php
function register()
{
  if (!empty($_POST)) {
    $msg = '';
    if ($_POST['user_name']) {
      if ($_POST['user_password_new']) {
        if ($_POST['user_password_new'] === $_POST['user_password_repeat']) {
          if (strlen($_POST['user_password_new']) > 5) {
            if (strlen($_POST['user_name']) < 65 && strlen($_POST['user_name']) > 1) {
              if (preg_match('/^[a-z\d]{2,64}$/i', $_POST['user_name'])) {
                $user = read_user($_POST['user_name']);
                if (!isset($user['user_name'])) {
                  if ($_POST['user_email']) {
                    if (strlen($_POST['user_email'] < 65)) {
                      if (filter_var($_POST['user_email'], FILTER_VALIDATE_EMAIL)) {
                        create_user();
                        $_SESSION['msg'] = 'You are now registered so please login';
                        header('Location: '.$_SERVER['PHP_SELF']);
                        exit();
                      } else $msg = 'You must provide a valid email address';
                    } else $msg = 'Email must be less than 64 characters';
                  } else $msg = 'Email cannot be empty';
                } else $msg = 'Username already exists';
              } else $msg = 'Username must be only a-z, A-Z, 0-9';
            } else $msg = 'Username must be between 2 and 64 characters';
          } else $msg = 'Password must be at least 6 characters';
        } else $msg = 'Passwords do not match';
      } else $msg = 'Empty Password';
    } else $msg = 'Empty Username';
    $_SESSION['msg'] = $msg;
  }
  return register_form();
}