Well first off, just to start the thread on a nice and depressing note...
http://www.koaa.com/news/miracle-child-born-without-brain-dies-in-pueblo/
(The baby in that video died this year at age 3 for those of you who don't feel like going to a random link given by a stranger on the internet).
As to your question, I presume the child has already been born for this question. If that is the case, I would go ahead and keep the child. The loving side of me could not kill a child and the cold/calculating side of me would realize that you're not surviving very long without a brain...
EDIT: BTW, since people keep asking about it (and I presume they didn't watch that video if they're asking...):
According to medical science, the child should not be able to hear or see anything (he only has the brain stem, which shouldn't be able to process that stuff). The child is medically, completely brain dead...HOWEVER, Nicholas was responding to people talking to him (not like, talking back but smiling and acting like a new-born). The doctors couldn't explain it but the child isn't just a bag of flesh in this case. I don't know if that will affect people's decision but I figured I would throw it out there. Also, I am taking the videos word for it so I suppose that could just be the reporter "spicing" the story up.