Hi chschenk, and thanks for looking into the problem for me. Your form worked for me so I started looking at my own form. Turns out the problem was caused by one of my input’s being called ‘name’. Try this:
<?php
/*
Template Name: Form
*/
?>
<?php get_header(); ?>
<?php echo 'We have got: ' . $_POST['name'] . ''; ?>
<form action="" method="POST">
<input type="text" name="name" value="test"/>
<input type="submit" name="submit" value="Submit"/>
</form>
<?php get_footer(); ?>
On my WordPress install this produces a 404 error page.