When people discuss parts of the body falling asleep, they are generally referring to tingling or numbness in those body parts. That tingling or numbness can be caused by a number of things, but is most commonly caused by either cutting off blood flow or nerve damage, and it is not recommended to attempt to make it happen intentionally.
There are easily accessible major veins and nerves running through the arms, which makes accidentally cutting off blood flow and pinching nerves remarkably easy. If there is persistent tingling or numbness, especially in the feet and hands or up the arms and legs, there may be nerve damage due to diabetes, autoimmune diseases or systemic diseases such as liver disease, among other causes. It is important that persistent tingling or numbness be mentioned to the family doctor for diagnosis.
In the absence of persistent tingling or numbness due to illness or disease, the most common reason for hands falling asleep is cutting off the blood flow or pinching a nerve. This can be done by sitting on the hands and certain ways of laying on the arms, especially when sleeping. Additionally, a person often can't notice he has cut off blood to his hands or put pressure on a nerve for several minutes, so positions that would be fine for a few minutes become a problem after several hours.