How do I find out what my iBooks "authorized computers" are? I saw a "Free" book on iBooks today and decided to download it.  I've never used iBooks before.

After it downloaded (and I entered my password), I clicked "Read", and iBooks said:


  Computer authorization was successful.
  
  You have authorized 2 computers out of your available 5.


I only have one Mac here.  (iBooks seems to be new with OS X 10.9, and this is the only Mac I've ever owned that is even capable of running 10.9.)  Is it including my old iPod Touch as a "computer"?  If not, how can I figure out what the other "authorized computer" is?
The iBooks authorization count is the same count you get for iTunes Store. They're the same thing. This covers Books, Music, Movies, etc... If you go to the Store menu item from iTunes or iBooks you can click View My Apple ID, enter your password and then you'll see the authorization count.

Basically if you have authorized another computer to use iTunes Store it counts as a computer authorized for that Apple ID. That's why you're seeing the count as 2. It's no longer just related to music. As Apple's info states on the Account Information screen:


  2 computers are authorized to use content purchased with this Apple ID


If you want to reset this, just click the Deauthorize All button and you can re-authorize your 1 computer to start fresh. You won't be able to see what computer it is, but you can see the count and reset it.