Wow, I'd have to disagree with a lot of the answers given.
First off, lets assume we're talking about Type 2 diabetes, which is where your body's insulin loses its effectiveness, and cannot clear sugar from the blood effectively. Over time, this may wear out the pancreas (where insulin is made) so it can never make enough, but caught early and treated this is certainly not a given.
Type 1 (often called juvenile onset) is where your body's immune system attacks your insulin making cells (beta cells) in your pancreas, and you lose the ability to make insulin. Type 1 diabetes is a VERY DIFFERENT PROCESS than type 2 diabetes (even though the result is the same, high blood sugars). Type 1 diabetes cannot be cured.
Type 2 diabetes can, in my opinion, be cured. By that I mean a person previously diagnosed with type 2 diabetes can reach a point where they do not meet any of the diagnostic criteria for diabetes, and are on no medications for it either. I'm not sure what people consider a cure, but I would count this type of situation as a cure. I've had several patients who changed their life, ate right, exercised, lost weight, and "cured" their diabetes.
Type 2 diabetes has a lot of additive causes, including weight-associated larger fat cells which interfere with insulin efficiency, lack of exercise which does the same, and high carbohydrate diets that keep insulin levels too high. So by changing those things, you can get the system working normally again, and in some cases, the diabetes really does go away. Cure.