WordPress nav menu without lists.

nav_walker_nav_menu.php

<?php

class v12_Walker_Nav_Menu extends Walker_Nav_Menu {

	function __construct() {
		add_filter( 'wp_nav_menu_args', array( __CLASS__, 'items_wrap' ) );
	}

	/**
	 * @see wp_nav_menu()
	 *
	 * @param array $args Arguments for wp_nav_menu
	 */
	static function items_wrap( $args ) {
		$args['container'] = '';
		$args['items_wrap'] = '<nav id="%1$s" class="%2$s">%3$s</nav>';
		$args['fallback_cb'] = '__return_false';
		return $args;
	}

	/**
	 * @see Walker::start_lvl()
	 * @since 3.0.0
	 *
	 * @param string $output Passed by reference. Used to append additional content.
	 * @param int $depth Depth of page. Used for padding.
	 */
	function start_lvl( &$output, $depth = 0, $args = array() ) {
		$indent = str_repeat("\t", $depth);
		$output .= "\n$indent<div class=\"sub-menu\">\n";
	}

	/**
	 * @see Walker::end_lvl()
	 * @since 3.0.0
	 *
	 * @param string $output Passed by reference. Used to append additional content.
	 * @param int $depth Depth of page. Used for padding.
	 */
	function end_lvl( &$output, $depth = 0, $args = array() ) {
		$indent = str_repeat("\t", $depth);
		$output .= "$indent</div>\n";
	}

	/**
	 * @see Walker::start_el()
	 * @since 3.0.0
	 *
	 * @param string $output Passed by reference. Used to append additional content.
	 * @param object $item Menu item data object.
	 * @param int $depth Depth of menu item. Used for padding.
	 * @param int $current_page Menu item ID.
	 * @param object $args
	 */
	function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
		$indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

		$class_names = $value = '';

		$classes = empty( $item->classes ) ? array() : (array) $item->classes;
		$classes[] = 'menu-item-' . $item->ID;

		$class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
		$class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';

		$id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
		$id = $id ? ' id="' . esc_attr( $id ) . '"' : '';

		$attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
		$attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
		$attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
		$attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';
		$attributes .= $id . $value . $class_names;

		$item_output = ! empty( $args->before ) ? $args->before : '';
		$item_output .= '<a'. $attributes .'>';
		$item_output .= ! empty( $args->links_before ) ? $args->links_before : '';
		$item_output .= apply_filters( 'the_title', $item->title, $item->ID );
		$item_output .= ! empty( $args->links_after ) ? $args->links_after : '';
		$item_output .= '</a>';
		$item_output .= ! empty( $args->after ) ? $args->after : '';

		$output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
	}

	/**
	 * @see Walker::end_el()
	 * @since 3.0.0
	 *
	 * @param string $output Passed by reference. Used to append additional content.
	 * @param object $item Page data object. Not used.
	 * @param int $depth Depth of page. Not Used.
	 */
	function end_el( &$output, $item, $depth = 0, $args = array() ) {
		$output .= "\n";
	}
}