The Feejee Mermaid is apparently currently on display as part of the American Museum of Natural History's exhibit on Mythic Creatures
. A Flickr user, despite being told that photography was forbidden in the exhibit, managed to surreptitiously snap a picture of it anyway
The one time I saw the Feejee Mermaid was back in 1998 when it was housed at Harvard's Peabody Museum. It wasn't on display, so I had to ask for special permission to see it back in the archives. I managed to snap a few pictures of it, despite also being told that photography was not allowed. I always wondered what the big deal was about taking pictures of it.
Anyway, I have a pretty thorough description of the Feejee Mermaid
and its history in the Hoaxipedia. The irony is that the creature currently on display as the original Feejee Mermaid almost certainly isn't. The original probably was destroyed when Moses Kimball's Boston Museum burned down in the 1880s.