gistfile1.php

<?php
add_filter( 'wp_nav_menu_objects', 'tgm_filter_menu_class', 10, 2 );
/**
 * Filters the first and last nav menu objects in your menus
 * to add custom classes.
 *
 * This also supports nested menus.
 *
 * @since 1.0.0
 *
 * @param array $objects   An array of nav menu objects.
 * @param object $args     Nav menu object args.
 * @return object $objects Amended array of nav menu objects with new class.
 */
function tgm_filter_menu_class( $objects, $args ) {

    // Add first/last classes to nested menu items.
    $ids        = array();
    $parent_ids = array();
    $top_ids    = array();
    foreach ( $objects as $i => $object ) {
        // If there is no menu item parent, store the ID and skip over the object.
        if ( 0 == $object->menu_item_parent ) {
            $top_ids[$i] = $object;
            continue;
        }

        // Add first item class to nested menus.
        if ( ! in_array( $object->menu_item_parent, $ids ) ) {
            $objects[$i]->classes[] = 'first-menu-item';
            $ids[]                  = $object->menu_item_parent;
        }

        // If we have just added the first menu item class, skip over adding the ID.
        if ( in_array( 'first-menu-item', $object->classes ) ) {
            continue;
        }

        // Store the menu parent IDs in an array.
        $parent_ids[$i] = $object->menu_item_parent;
    }

    // Remove any duplicate values and pull out the last menu item.
    $sanitized_parent_ids = array_unique( array_reverse( $parent_ids, true ) );

    // Loop through the IDs and add the last menu item class to the appropriate objects.
    foreach ( $sanitized_parent_ids as $i => $id ) {
        $objects[$i]->classes[] = 'last-menu-item';
    }

    // Finish it off by adding classes to the top level menu items.
    $objects[1]->classes[] = 'first-menu-item'; // We can be assured 1 will be the first item in the menu. :-)
    $objects[end( array_keys( $top_ids ) )]->classes[] = 'last-menu-item';

    // Return the menu objects.
    return $objects;

}

Thanks for the filter, I have been using it for sometime now.

I just started getting the following error:
"Strict Standards: Only variables should be passed by reference on line 53".

The issue was resolved by replacing line 53:

$objects[end( array_keys( $top_ids ) )]->classes[] = 'last-menu-item';

with the following two lines:

$top_ids_array_keys = array_keys($top_ids);
$objects[end( $top_ids_array_keys )]->classes[] = 'last-menu-item';