Couple of thoughts from your comments.

1. It seems to be getting worse, so you'll want to deal with it.
2. It's unlikely to be circulatory. Circulation (vascular) problems come on quickly and leave quickly once the pressure is gone. Having something for a couple of hours is more likely nerve compression (which actually is a circulatory problem, but that's more detail than we need).
3. You didn't say where in your hand you feel the tingling, try to be aware of its in your palm, your fingers (and which ones). This will be helpful to try to narrow down the likely spot of compression if you need to see someone about it.
4. Generally numb hands are caused by compression on the nerve that runs down the middle of your wrist (median nerve), typically as it goes through a small tunnel in your wrist called the carpal tunnel. Lots of other stuff runs through this tunnel, including the ligaments of various muscles. A little bit of swelling here or compression can give you the hand symptoms. Many of the solutions people are posting deal with shifting your body such that less weight his put on your hands. White knuckle riding can also increase the pressure. Be aware of how tightly you grip the bars.
5. I'd suggest doing a few things: If it persists consult a chiropractor, MD or PT with sports medicine experience.
4. Stretching your forearms out from time to time and work out any knots you may find in the muscles can sometimes help a bit. http://www.nqi.ca/chww/downloads/200...ms%20final.pdf
5. Play around with your seat, handlebar height and position to see if it helps as per the suggestions others have posted.
6. You could try changing your hand position from time to time or riding hands free for a bit to give yourself a break. I do this even on short rides.

Hope that helps a bit. The preceding is intended for information only and does not represent a diagnosis or recommendation for care.

yep...