LinkedIn button
LinkedIn sets their login cookie to be persistant, and also does not set the secure flag, so that it will be sent back to them whenever a user visits any page that has a LinkedIn profile or share button on it. This is similar to how the Facebook "like" button works, although LinkedIn seem to rely on getting the URL of the visited page through the Referer: header, while Facebook has it encoded in the query string (also). Normally login cookies expire at the end of a session, or after a short period, as they are only normally needed to maintain state during a logged in session.
This technique lets social network sites build up a record of the sites you visit and associate it with your login profile, so you can be targeted with ads etc.