When Facebook rolled out the subscription services, I immediately approved it while not knowing exactly what would change. I learned it allowed non-friends to subscribe to my updates, even when I didn't accept their friend requests. Having no need for this, I wanted to disable it, but nowhere in the account or privacy settings could I find the section on subscriptions. Here's how to prevent people from subscribing to your content:
1) Go to your profile (not the newsfeed, your actual profile page that someone sees to learn about you).
2) Click on "Subscribers" on the left-hand menu.
3) On the page that opens up, you should see a button "Edit Settings" in the upper-right. Click it.
4) In the first section "Subscribers" change the drop-down option from "On" to "Off".
There you go!
UPDATE: For the new time line, you'll find "Subscribers" under the down-arrow menu to the right of your name at the top of your profile (and just below your cover photo).
1) Go to your profile (not the newsfeed, your actual profile page that someone sees to learn about you).
2) Click on "Subscribers" on the left-hand menu.
3) On the page that opens up, you should see a button "Edit Settings" in the upper-right. Click it.
4) In the first section "Subscribers" change the drop-down option from "On" to "Off".
There you go!
UPDATE: For the new time line, you'll find "Subscribers" under the down-arrow menu to the right of your name at the top of your profile (and just below your cover photo).