Add custom attributes to menu items without plugin

Filter nav_menu_link_attributes:

add_filter( 'nav_menu_link_attributes', 'wpse_100726_extra_atts', 10, 3 );

function wpse_100726_extra_atts( $atts, $item, $args )
{
    // inspect $item, then …
    $atts['custom'] = 'some value';
    return $atts;
}

This works with WordPress < 3.6:

add_filter( 'walker_nav_menu_start_el', function( $item ) {

    $parts = explode( '>', $item );
    $out   = array ();

    foreach ( $parts as $i => $part )
    {
        if ( 0 === strpos( $part, '<a ' ) ) // a start
            $out[ $i ] = $part . ' data-foo="bar"';
        else
            $out[ $i ] = $part;
    }

    return join( '>', $out );
});