It's important to remember that this function does NOT replace newlines with <br> tags. Rather, it inserts a <br> tag before each newline, but it still preserves the newlines themselves! This caused problems for me regarding a function I was writing -- I forgot the newlines were still being preserved.
If you don't want newlines, do:
<?php
$Result = str_replace( "\n", '<br />', $Text );
?>