My hands feel like they are asleep a lot of the time. What can this mean?

HAnd Nerve. Three different nerves supply sensation to the hand, compression or injury to these anywhere along their routes can give symptoms. Where and how is what the diagnosis is. Where and how is why many seek the attention of a hand surgeon for diagnosis and treatment.
Neuropathy. Carpal tunnel syndrome is a very common neuropathy or nerve damage, similar to bumping your funny bone. This can be due to compression of median nerve in carpal tunnel. Poorly controlled diabetes as well as some vitamin deficiencies can also cause peripheral neuropathy although more commonly in feet. Go see your family doc who may order a nerve conduction velocity test if diagnosis isn't clear.