There are no foods that diabetics truly "can't" eat, but there is a recommended diet high in the following foods. This list will never include refined sugars, simple starches or simple carbohydrates as they are not good choices for a diabetic diet.
Fiber actually helps the body process sugar, which is why most fruit is good for the body; there is substantial sugar, but the fiber processes it out (barring those with an unusually high concentration of fructose, like raisins or dried fruits).
Because whole grains are slower to digest, they deliver energy (sugar) to the body, but do so over a longer time frame that the body can adjust to and work with rather than a dumping of refined sugar that is almost instantly digested.
Protein is essential for any healthy diet because it promotes muscle development and healthy oil production. It is also low in glucose.
Vegetables, because of their generally low glycemic index, are excellent choices for any diabetic diet, and deliver essential nutrients and vitamins to the body.
Low Glycemic Index
Any food with a low glycemic index will not have a significant impact on your blood sugar. Many brands offer "GI" symbols to show foods with a low glycemic index, or lists are available online (see Resources below).