One might want to be noted that the browsers are case-sensitive to the $path parameter.
For example, if you do this:
<?php
session_set_cookie_params(0,"/webapp/");
session_start();
?>
and you visit your site in this way:
example.com/WebApp/
You would get a new session on every request.
I'm not sure if this is the standard, but I see this happens on IE 6, Firefox 12 (Palemoon, actually), Chrome 19 (Portable version), and on both IIS and Apache.