If you are using Apache, you can do a neat little trick with your .htaccess file to drop the "?" from the query string (which is what it sounds like you would like to do).
There is an article about this on phpbuilder by Tim.
basically, you add the following to a .htaccess file in the folder where your php script will be, the root directory in your case:
<Files home>
ForceType application/x-httpd-php
</Files>
The ForceType directive will treat what looks like a folder as a file. So this url would in fact pass two querystring values to the script "home" (note the absence of .php)
www.mysite.com/home/arg1/arg2
It works because Apache will "regress" back down a url until it finds a valid folder--which in this case in actually a php file (I may have paraphrased this incorrectly, but this is my understanding). The only other trick is to get the variables out of your url and treat them as if they were in a querystring:
$querystring=explode("/",$_SERVER['PHP_SELF']);
This will create an array with the following:
$querystring[0]--ignore this, the leading slash
$querystring[1]--this is your script name
$querystring[2]--argument 1
$querystring[3]--argument 2
etc...
Your script page will have to be designed to take a certain action based on the number of folders (arguments) in the URL--including no arguments, which is your default page.
The challenge in your instance in applying this idea to a root level folder so that it will occur for www.site.org and not www.site.org/script
I'm pretty sure this will not work for a root folder, but I haven't tried it:
<Files>
ForceType application/x-httpd-php
</Files>
You could try index for your script name, but I'd guess it will result in www.site.org/index