UPDATE 2011 March 8: A commenter reports dragging the pictcliped image into PowerPoint allows you save the image from there, possibly in other formats. I cannot test this as I do not have this setup. It appears however that the latest version of iTunes, at least, no longer creates these when copying album art out of the app.
UPDATE 2010 July 4: This process no longer works with 10.6 (.3 for me) as reported by readers. It seems that Apple found this feature and killed it. However there is a simple workaround. See the section for 10.6.3
For versions of OSX up to 10.6:
So a little annoying feature of some Apple/Mac apps is the creation of a image in the format “pictclipping”. Converting these to something usable is not so intuitive so I am posting it here as to be easily located for myself if for nobody else (though I imagine others are looking for this from time to time).
Anyway, the easiest way to do this seems to be to use the clipboard and the “Preview” application.
To do the conversion in this way, first double click the pictclipping image to open it in the finder. Next from the Finder’s “Edit” menu choose “Copy”. Next, launch the “Preview” application and from the “File” menu choose “New from clipboard”. Then using the “File” “Save as” menu options, save as any image type you like.
Pretty simple, but not something I would have thought of right away.
For versions of OSX after 10.6:
Ok, so it seems Apple did not like the feature of being able to coy a Picture Clipping so easily, using their own software. I have tried to figure out a solution and did some searching but without some purchased software, so far, it seems this is not possible. However, here is something you can do to hold you over till something is discovered.
Right click on the Picture Clipping, in the Finder, choose “Quick Look [NAME OF YOUR PICTURE CLIPPING HERE]” to view the full sized image in the Finder Quick Look previewer app. Then use the selective screenshot tool to grab just the image. If not familiar with this process: with the Picture Clipping image up, choose the [command] key at the same time as the [shift] key and then press the  key. This will bring up a small crossed lines (not sure how to explain it, think crosshairs for targeting something) pointer. Use this to hilight just the portion of the picture clipping in the preview that you wish to copy. When you release the pointer this image will be on the desktop as a PNG file with a name like “Screen shot 2010-07-04 at 5.16.53 AM”. Simply rename this file to something useful like “my-album-art.png” and you are done.
Hope something better appears. I will keep looking for something.