Count singular post views automatically

You could hook into template_redirect and execute a helper function:

add_action( 'template_redirect', 'wpse_75558_count' );

function wpse_75558_count()
{
    if ( is_singular() )
        setPostViews( get_the_ID() );
}

To display the post views, you have to use a later hook. I would recommend the_content:

add_filter( 'the_content', 'wpse_75558_show_count' );

function wpse_75558_show_count( $content )
{
    $count = getPostViews( get_the_ID() );

    if ( ! is_numeric( $count ) )
        $count=""; // prevent errors showing to visitors
    else
        $count = "<p class="view-count">Views: $count</p>";

    return $content . $count;
}

Just an idea, I haven’t tested the code.