How to set HTML attributes for each individual selection created by Forms API when creating a dropdown list?

I just want to say thanks for your guidance.

I was able to do what I wanted based in great part to your guidance.

For those that want to do this in the future here is how I did it:

1) Override the theme_select() function by adding a new function to your theme's template.php file and replace the word "theme" in the declaration of the function with the name of your theme. For example, if youa re using the Garland theme, the new name of the function would be garland_select() as the example below will show. The code should initially be an exact copy of the actual theme_select() function which you can get from the API reference guide (api.drupal.org).

2) Create a new version of the form_select_options() function within the same template.php file. You can call it myform_select_options. The code should initially be an exact copy of the actual form_select_options() function which you can get from the API reference guide (api.drupal.org).

3) Look at the code in the function you created in step one and instead of calling the original form_select_options on the last line, have it call your new one (myform_select_options).

4) Modify the new myform_select_options to build each entry of the select box to your liking.

Below are the functions that I used to accomplish this. Note that all I wanted to do what add "class="levelx"" to each option where x was the depth level. In another function using Forms API, I add "-" (hyphens) to symbolize depth and be displayed more deeply to the user, so I just went in and counted "-" with the PHP function substr_count() to let me know what level the entries are found in and then divide by 2 since I added two "-" every time I needed to display an entry at a deeper level. Don't worry about this too much since this is my own need. You will modify the new myform_select_options() function to do what YOU need it to do.

Here they are (if you copy and paste them, do not include the php tags at the beginning and end of each example since those should already exist in your templete.php file, I added them for enabling color coding):

Just below is the overridden theme_select() function in my theme's template.php file. Note the new garland name when it is declared. This is just an example that uses the garland theme. You must replace this with your theme's name (step one above). Also note that the last line calls my new version of the form_select_options() function called myform_select_options() which I show you below.

<?php
/**
 * Overriding theme_select() function to format the individual items in a select box
 *
 */
function garland_select($element) {
  $select = '';
  $size = $element['#size'] ? ' size="' . $element['#size'] . '"' : '';
  _form_set_class($element, array('form-select'));
  $multiple = isset($element['#multiple']) && $element['#multiple'];
  return theme('form_element', $element, '<select name="'. $element['#name'] .''. ($multiple ? '[]' : '') .'"'. ($multiple ? ' multiple="multiple" ' : '') . drupal_attributes($element['#attributes']) .' id="'. $element['#id'] .'" '. $size .'>'. myform_select_options($element) .'</select>');
}
?>

Just below is the custom form_select_options() function in my theme's template.php file. Note that I only modified the instruction just before "return $options;" because that is what I needed to affect. You may be looking to modify something else.

<?php
/**
 * Calling alternative form_select_options() function to format the individual items in a select box
 *
 */
function myform_select_options($element, $choices = NULL) {
  if (!isset($choices)) {
    $choices = $element['#options'];
  }
  // array_key_exists() accommodates the rare event where $element['#value'] is NULL.
  // isset() fails in this situation.
  $value_valid = isset($element['#value']) || array_key_exists('#value', $element);
  $value_is_array = is_array($element['#value']);
  $options = '';
  foreach ($choices as $key => $choice) {
    if (is_array($choice)) {
      $options .= '<optgroup label="'. $key .'">';
      $options .= form_select_options($element, $choice);
      $options .= '</optgroup>';
    }
    elseif (is_object($choice)) {
      $options .= form_select_options($element, $choice->option);
    }
    else {
      $key = (string)$key;
      if ($value_valid && (!$value_is_array && (string)$element['#value'] === $key || ($value_is_array && in_array($key, $element['#value'])))) {
        $selected = ' selected="selected"';
      }
      else {
        $selected = '';
      }
      $options .= '<option value="'. check_plain($key) .'" class="level' . check_plain((substr_count($choice, '-')) / 2) . '"' . $selected .'>'. check_plain($choice) .'</option>';
    }
  }
  return $options;
}
?>

Thanks again to the folks above who helped to guide me.