How to prevent my Facebook session from being available to other sites?

I use Facebook with the “keep me signed in” / “remember me” option enabled. (I use the same personal laptop most of the time so it’s convenient)

However, when I visit other sites like cnn.com I wound not want to “Like” any pages or do anything else which can link to my Facebook profile.

However, cnn.com automatically shows “Friend’s Activity” panel on the right which shows my Facebook friends listed and their activities on the site. (I do not have a login on cnn site.)

My concern however is not just about CNN.com but with all sites in general – who may try to use my Facebook session / cookies / login credentials to link my activity to my profile. I simply do not want any of this.

How can I prevent my Facebook login from being read and used in this way by other syndicated sites?

Thanks in advance.

PS: I have already turned off Instant Personalization under Privacy Settings. Just now, I also turned off “Info accessible through your friends” and did a quick check – doesn’t seem to have made a difference on cnn.com