I thought this was an easy question at first, till i tried it! and you are right, in previous versions all you had to was copy and paste the image into Acrobat and it worked. What it used to do was create the image as a stamp.
It looks to me that in Acrobat X they have stopped you pasting images from external programs, i tried a number of programs but to know joy. You can copy images from within Acrobat to your hearts content, just not from outside! I have a good workround tho! (It works!)
After copying the image from outside of Acrobat, If you are running Acrobat X Pro or Standard, chose Create – PDF from clipboard. Then, on the right hand side under Tools, Content, chose Edit object. Select the image and now COPY again(its now inside Acrobat!), then go to the other PDF and then you can PASTE as many as you want!
Only takes a few more seconds longer but agree its a bit annoying, but hey, it works!
Hope this helps?