There are many security vulnerabilities in what you are trying to achieve, I will suggest that you read up on some of them. To answer your question though, as per comments above, type is wrong, should be something like "text, list" etc.
You should also invoke the form action once submit has been selected (also don't see any form closing method), change your code -
<?php
if( $_GET["cpr"] || $_GET["password"] ) {
echo "CPR ". $_GET['cpr']. "<br />";
echo "Kodeord ". $_GET['password'];
exit();
}
?>
<html>
<body>
<form action = "<?php $_PHP_SELF ?>" method = "GET">
CPR-NR: <input type = "text" name = "cpr" />
Kodeord: <input type = "password" name = "password" />
<input type = "submit" />
</form>
</body>
</html>
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