There are some studies on mice. They were given raspberry ketone, and it appeared to prevent weight gain when the little rodents were fed high-fat diets. Apparently the anti-obesity effects were due to stimulation of lipolysis (which is how the body breaks down fat in fat cells called adipocytes) in both regular fat tissue and brown fat tissue. It also suppressed release of pancreatic lipase -- a digestive enzyme needed to break down dietary fats so they can be absorbed through the small intestinal wall.
But this research was done on mice. We're humans, not rodents. We have different physiology and different emotional reasons for eating (or not eating) fats and other foods. So just because mice didn't get fat doesn't mean raspberry ketone will work the same way in humans. We need clinical research to know that, and I can't find any research on people.
So will it hurt you to take raspberry ketone supplements? Probably not. Will it help you lose weight? I don't know, but I doubt it. More than likely it will just make your wallet a little lighter.
Our Alternative Medicine Guide at About.com, Dr. Cathy Wong has written in depth about raspberry ketones.