I think this could get resource-intensive quickly, but fastest API way would be to create list of tags and query for posts that do not belong to any:
$tags = get_tags();
$ids = array();
foreach ( $tags as $tag )
$ids[] = $tag->term_id;
$posts = get_posts( array( 'tag__not_in' => $ids ) );
If you have large amount of tags or need to do this often it is probably better to look into building raw SQL query for this.
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