Wordpress - How do you remove hard coded thumbnail image dimensions?

Related: Filter to remove image dimension attributes?

There's a filter on post_thumbnail_html which receives as its argument the full html element representing the post thumbnail image before it's echoed to the page. You can filter out the dimensions with a bit of regex:

add_filter( 'post_thumbnail_html', 'remove_thumbnail_dimensions', 10, 3 );

function remove_thumbnail_dimensions( $html, $post_id, $post_image_id ) {
    $html = preg_replace( '/(width|height)=\"\d*\"\s/', "", $html );
    return $html;
}

you could just grab the url of the thumb and put it in an img tag yourself:

<?php
$thumbnail = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ), 'your_thumb_handle' );
?>
<img src="<?php echo $thumbnail['0']; ?>" />