List Sub-Pages
Versions prior to WordPress 2.0.1:

Put this inside the the_post() section of the page.php template of your WordPress theme after the_content(), or put it in a copy of the page.php template that you use for pages that have sub-pages:

<ul>
	<?php
	global $id;
	wp_list_pages( array(
		'title_li'    => '',
		'child_of'    => $id,
		'show_date'   => 'modified',
		'date_format' => $date_format
	) );
	?>
</ul>

This example does not work with WordPress 2.0.1 or newer if placed in a page template because the global $id is not set. Use the following code instead.

WordPress 2.0.1 or newer:

NOTE: Requires an HTML list tag (either <ul> or <ol>) even if there are no subpages. Keep this in mind if you are using CSS to style the list.

<ul>
	<?php
	wp_list_pages( array(
		'title_li'    => '',
		'child_of'    => $post->ID,
		'show_date'   => 'modified',
		'date_format' => $date_format
	) );
	?>
</ul>

The following example will generate a list only if there are child pages (pages that designate the current page as a parent) for the current page:

<?php
$children = wp_list_pages( 'title_li=&child_of='.$post->ID.'&echo=0' );
if ( $children) : ?>
	<ul>
		<?php echo $children; ?>
	</ul>
<?php endif; ?>

List members of a custom post type
If a given custom post type is hierarchical in nature, then wp_list_pages() can be used to list the member of that custom post type. In this example the custom post type Portfolio is listed:

$args = array(
	'post_type' => 'portfolio',
	'title_li'  => __( 'Portfolio', 'textdomain' )
);
wp_list_pages( $args ); 

List subpages even if on a subpage

The above examples will only show the children from the parent page, but not when actually on a child page. This code will show the child pages, and only the child pages, when on a parent or on one of the children.

This code will not work if placed after a widget block in the sidebar.

<?php
if ( $post->post_parent ) {
	$children = wp_list_pages( array(
		'title_li' => '',
		'child_of' => $post->post_parent,
		'echo'     => 0
	) );
} else {
	$children = wp_list_pages( array(
		'title_li' => '',
		'child_of' => $post->ID,
		'echo'     => 0
	) );
}

if ( $children ) : ?>
	<ul>
		<?php echo $children; ?>
	</ul>
<?php endif; ?>

As an alternative, this code in a sidebar.php, displays only top level pages, but when viewing a page that has children (or is a child) it displays only children of that parent.

When visiting main page, all top level pages are listed in the sidebar.
When visiting a top level page with no children, all top level pages are listed.
When visiting a top level page with children, just the children pages, and descendant pages, are listed.
When visiting a child page, just the children, and descendant pages, of that parent, are listed.

$output = wp_list_pages( array(
	'echo'     => 0,
	'depth'    => 1,
	'title_li' => '<h2>' . __( 'Top Level Pages', 'textdomain' ) . '</h2>'
) );

if ( is_page() ) {
	$page = $post->ID;
	if ( $post->post_parent ) {
		$page = $post->post_parent;
	}

	$children = wp_list_pages( array(
		'echo'     => 0,
		'child_of' => $page,
		'title_li' => ''
	) );

	if ( $children ) {
		$output = wp_list_pages( array(
			'echo' => 0,
			'child_of' => $page,
			'title_li' => '<h2>' . __( 'Child Pages', 'textdomain' ) . '</h2>'
		) );
	}
}
echo $output;

Page list that only displays if child (sub) pages exist, displays page list of subpages on the parent page AND on the child pages
However this code keeps the parent page name in the title which makes it different from the previous example.

<?php
if ( $post->post_parent ) {
	$children = wp_list_pages( array(
		'title_li' => '',
		'child_of' => $post->post_parent,
		'echo'     => 0
	) );
	$title = get_the_title( $post->post_parent );
} else {
	$children = wp_list_pages( array(
		'title_li' => '',
		'child_of' => $post->ID,
		'echo'     => 0
	) );
	$title = get_the_title( $post->ID );
}

if ( $children ) : ?>
	<h2><?php echo $title; ?></h2>
	<ul>
		<?php echo $children; ?>
	</ul>
<?php endif; ?>

Sort Pages by Post Date
This example displays Pages sorted by (creation) date, and shows the date next to each page list item.

<ul>
	<?php wp_list_pages( 'sort_column=post_date&show_date=created' ); ?>
</ul>

List all top-level pages and subpages only of this parent

The following lists all top-level pages and

if on a top level page – children of only this page
if on a subpage – its siblings but not children of other top pages

$ancestor_id = 1843; // you want to change this
$descendants = get_pages( array( 'child_of' => $ancestor_id ) );
$incl = '';

foreach ( $descendants as $page ) {
	if ( ( $page->post_parent == $ancestor_id )
		|| ( $page->post_parent == $post->post_parent )
		|| ( $page->post_parent == $post->ID )
	) {
		$incl .= $page->ID . ",";
	}
}
?>

<ul>
	<?php
	wp_list_pages( array(
		'child_of'    => $ancestor_id,
		'include'     => $incl,
		'link_before' => '',
		'title_li'    => '',
		'sort_column' => 'menu_order'
	) );
	?>
</ul>

List parent page and all descendant pages

Since there’s no way to tell wp_list_pages to display a particular parent tree (parent and all generations displayes) this example uses get_pages to get all the descendants for a parent, then use wp_list_pages to display the ‘family tree’.

<?php 
// Use wp_list_pages to display parent and all child pages all generations (a tree with parent).
$parent = 93;
$args   = array( 'child_of' => $parent );
$pages  = get_pages( $args );

if ( $pages ) {
	$pageids = array();
	foreach ( $pages as $page ) {
		$pageids[] = $page->ID;
	}

	$args = array(
		'title_li' => sprintf( __( 'Tree of Parent Page %s', 'textdomain' ), $parent ),
		'include'  =>  $parent . ',' . implode( ",", $pageids )
	);
	wp_list_pages( $args );
}
?>

List topmost ancestor and its immediate children

This method will show the topmost ancestor of the current page as well as the topmost ancestor’s immediate children. This can be used for clean secondary subnavigation.

First, create the following function (preferably in functions.php, assuming this is for a theme):

if ( ! function_exists( 'wpdocs_get_post_top_ancestor_id' ) ) {
/**
 * Gets the id of the topmost ancestor of the current page.
 *
 * Returns the current page's id if there is no parent.
 * 
 * @return int ID of the top ancestor page.
 */
function wpdocs_get_post_top_ancestor_id() {
	if ( ! $post = get_post() ) {
		return;
	}
    
	$top_ancestor = $post->ID;
    if ( $post->post_parent ) {
        $ancestors = array_reverse( get_post_ancestors( $post->ID ) );
        $top_ancestor = $ancestors[0];
    }
    
    return $top_ancestor;
}
} // Exists.

Next, add the following code to your theme (wherever you want the menu to appear):

<ul class="clearfix">
	<?php
	wp_list_pages( array(
		'title_li' => '',
		'include'  => wdocs_get_post_top_ancestor_id()
	) );
	
	wp_list_pages( array(
		'title_li' => '',
		'depth'    => 1,
		'child_of' => wpdocs_get_post_top_ancestor_id()
	) );
	?>
</ul>