@splashingpixels - That solution wasn't working for me, but I figured out why in the meantime. The solution code you offered in the first reply is working indeed, but in my case it had to be placed in header.php (themefile) instead of functions.php. As told I tried that before, but entered it outside an if-statement where is had to be inside, so that's why it wasn't working.
Conclusion:
remove_action( 'woocommerce_before_main_content', 'woocommerce_breadcrumb', 20, 0)
is working fine, but you might have to insert it in another file then functions.php (and properly insert it of course ;-) )