Count posts or custom post types from last 24 hours (or from today)

You can write your own function (add it to functions.php file:

function get_posts_count_from_last_24h($post_type="post") {
    global $wpdb;

    $numposts = $wpdb->get_var(
        $wpdb->prepare(
            "SELECT COUNT(ID) ".
            "FROM {$wpdb->posts} ".
            "WHERE ".
                "post_status="publish" ".
                "AND post_type= %s ".
                "AND post_date> %s",
            $post_type, date('Y-m-d H:i:s', strtotime('-24 hours'))
        )
    );
    return $numposts;
}

function get_posts_count_from_today($post_type="post") {
    global $wpdb;

    $numposts = $wpdb->get_var(
        $wpdb->prepare(
            "SELECT COUNT(ID) ".
            "FROM {$wpdb->posts} ".
            "WHERE post_status="publish" ".
                "AND post_type= %s ".
                "AND DATE_FORMAT(post_date, '%Y-%m-%d') = %s",
            $post_type, date('Y-m-d', time())
        )
    );
    return $numposts;
}

And then use it in template:

<?php echo get_posts_count_from_last_24h(); ?>
<?php echo get_posts_count_from_today(); ?>