Using WordPress core function wp_count_posts, you can easily display total number of posts. Here is a simple example on how to use this function:

<?php
	$count_posts = wp_count_posts();
	$published_posts = $count_posts->publish;
	echo 'We published ' . $published_posts . ' posts until now, and it's still growing..';
?>

This displays a text output like this;

We published 1908 posts until now, and it's still growing..

With wp_count_posts you also get other counts like drafts, requested posts etc. Here is a sample output showing what wp_count_posts returns as an Object:

stdClass Object
(
    [publish] => 1908
    [future] => 0
    [draft] => 9
    [pending] => 0
    [private] => 1
    [trash] => 0
    [auto-draft] => 19
    [inherit] => 0
    [request-pending] => 0
    [request-confirmed] => 0
    [request-failed] => 0
    [request-completed] => 0
)

In your theme, you can use any of those properties to display number of posts.