According to a post on the Official Google Blog:

Google is a company fueled by innovation, which to us means trying lots of new things all the time — and sometimes it means reconsidering our goals for a product. Later this week, we will stop accepting new questions in Google Answers, the very first project we worked on here.

They don’t give a specific reason, but from what I’ve read across the Internet it seems to be at least in part because of the explosive popularity of Yahoo! Answers.

It’ll be somewhat sad to see this product go. But it’s kind of like a floppy drive: you have a peace of mind knowing you have one in case you really need it, but you almost never end up using it.