I made the LiveJournal "ljsession" cookie set that attribute.
If you use IE6 SP1 (go get it from Windows Update if you use a different IE), then logout, and log back in to get the more secure cookie.
There's an RFE to get this added to Mozilla also:
http://bugzilla.mozilla.org/show_bug.cgi?id=178993
Go vote for it if you have a Bugzilla account.