Unless, however, you get lucky and find one that has the face of a man.
They're called jin men gyo; literally, human-faced fish. And look something like this:
Although that one looks more like a rabbit if you ask me.
My son had a friend in kindergarten who refused to walk to school because she had to cross a bridge with several jin men gyos in it. She was entirely freaked out by them.
In 1990 someone sent in a picture to a magazine and all of the sudden they became the fad all throughout Japan. Everyone was talking about them, taking pictures, making TV shows...
It was during that uproar a Japanese newspaper reported that the creepy fish were found in Korea as well. The paper below actually states there was a resurgence of human-faced fish in Korea after a fourteen year absence (I just think nobody was looking).
Here's a Korean news station with the news.
There is also this type of jin men gyo. As well as a neko men gyo, a carp with a cat face. The legend has it that at night it gets out of the pond and walks around.
Oh, and since we're on the subject of Japanese koi, I found this link. Which is just about the coolest thing I've seen all week. Although they do cost two hundred bucks.