The obvious suspect is pressure/weight on your hands - you're either carrying too much weight on a particular vascular structure (vein, artery, blood vessel) or you are pinching a nerve. Lack of blood flow (first explanation) can result in tingling/numbness as circulation is cut off/returns. Pinching a nerve, well, that's like "''my arm feel asleep" - at least to me.
Possible solutions - change hand position (more) often, change gloves and/or change/add handlebar tape/cushioning.
FWIW, I change hand positions regularly, tighten my grip on my handlebars, wiggle my fingers semi-constantly, and move from upright to in-the-drops riding positions semi-regularly (which changes the weight/pressure on my hands accordingly).