A simple function that outputs a cleaner one-level nav with classes intact.

cleanernav.php

/**
 * Returns a cleaner Navigation
 *
 * Usage:
 * <nav id="site-navigation" class="main-navigation" role="navigation">
 *     <?php cleanernav('primary'); ?>
 * </nav>
 *
 * Output Example:
 * <nav id="site-navigation" class="main-navigation" role="navigation">
 *      <a id="menu-item-64" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-64" href="http://localhost/about/">About</a>
 *      <a id="menu-item-61" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-64 current_page_item" href="http://localhost/blog/">Posts</a>
 *      <a id="menu-item-60" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-64" href="http://localhost/">Sample Page</a>
 * </nav>
 *
 */

function cleanernav($location) {
    $clearnav = wp_nav_menu(array(
                    'theme_location' => $location,
                    'container' => false,
                    'items_wrap' => '%3$s', 
                    'echo' => false,
                    ));

    $find = array('><a', 'li');
    $replace = array('','a');
    $newnav = str_replace($find, $replace, $clearnav);
    echo $newnav;
}