This is commonly solved by using a transparent GIF.
For example, on site1.com, include an image:
<img src="http://site2.com/mybug.php?segment1=data1&segment2=data2" height="0" width="0">
Site2 then sets a cookie (in mybug.php) that it will read on subsequent accesses to Site2, based on the name/value pairs in the querystring, and returns a transparent gif in the body of the http response.
This, for example, is how advertising targeting systems do their magic. It can be circumvented by browser security settings, and may require you to include a privacy policy file to work reliable.
The caveat is that you can't just trust this data on your server if it is at all sensitive; in other words, you don't want to use this to transmit usernames, passwords, or the like. If you want to send sensitive data you'll need to use a shared secret and use a reasonably secure encryption mechanism and encrypt at least the values.