Q:

How to export the contact photo in Mountain Lion? 

I want to use the photo of a contact in the Address Book/Contacts in another app.  What is the easiest way to export the contact photo in Mountain Lion to an image file?  Dragging it out to the desktop does not work for me: I always get the photo Resize window instead. 

A:

Trying on OS X Yosemite 10.10.1:
On OS X 10.8 it was possible to extract a photo from contacts on the Mac user interface. 
That did not work for me on the current version. 
Thus I went to look in the ~/Library. 
I found the picture I had taken under

~/Library/Application\ Support/AddressBook/Sources/(some long hex string)/Images/

Thus on Finder click the "Go To" menu, holding the ⌥ ALT.  Click on "Library", then navigate to the Images folder. 
(On my iPhone, in Contacts, I had taken a photo of a friend yesterday. 
Today I wanted to file the photo, found it as above on my Mac, though with a size of 87 KB only.) 

A:

Assuming Mountain Lion 10.8.2:

Click on the photo in Contacts
Click once to select the one you want from the resulting grid of available photos
Click on the icon with the pencil across it at the bottom left of the grid window. 
Click on the larger version of the image that appears, and copy the image to the clipboard. 

Assuming Mountain Lion 10.8.4:

Click on the photo in Contacts
Make sure the image opens in the large Pop-up underneath the small image. 
Click on the larger image. 
Copy the image to the clipboard, e.g. via command-C.

You can now paste the image anywhere you want.  
For example, you can open Preview and, when it's ready, select the menu File < New from Clipboard, and a new window will open with the photo in it.  You can then save that file in any format available to anywhere you wish.