How do you Query posts with nothing in common?

Maybe you’re looking for the post__in parameter in WP_Query.

$query = new WP_Query(array(
    'post__in' => array(23,18,2,199,6,8)
);

And then:

while ( $query->have_posts() ) {
    $query->the_post();
    /* post loop */
}

Take a look at the docs. =D

For public queries:

post__in is not public queryable by default, so you can just validate and copy $_GET['post__in'] on the parse_query action hook, and let the thing happen.

add_action('parse_query', 'wpse59828_parse_query');
function wpse59828_parse_query($query) {
    if (empty($_GET['post__in']))
        return $query;

    $posts = explode(',', $_GET['post__in']);
    $post__in = array();
    foreach ($posts as $p) {
        $post__in[] = intval($p);
    }

    $query->query_vars['post__in'] = $post__in;
    return $query;
}

Then you would just access this:

http://mywebsite.com/?post__in=23,18,2,199,6,8

Please note that, like this, you won’t be able to set the post order in WordPress versions before 3.5 (#13729). Use this plugin if you need to.