I would have someone check out your body position on your bike. You might have too much weight on your hands due to a geometry issue. Find a GOOD road bike shop or someone who knows bike geometry. There are some good rules of thumb out there for how to fit a bike but it's all about how it feels so even if your bike was set up right you might want to do some tweaking.

Also, how is your bar tape? Fresh? Worn out? Consider what type of road you were on. I did a 60 mile race on agressive chipseal and I couldn't feel my hands for about an hour after the race was over. lastly, I find that putting the center of my palm right on the top of the shift levers (the pointy part) for a while helps relax my hands, kind of like a golf ball under the arch of your foot after a long run.

It is the ulnar nerve (http://en.wikipedia.org/wiki/Deep_branch_of_ulnar_nerve). Read more about cycling and the ulnar nerve here and here.

For a cheap first option fix, try some gloves with padding in the palm designed to take pressure of the nerves like the Pearl Izumi Pittards. Next, you could try installing some handlebar gel and new thicker bar wrap on your bars. I bet new gloves, gel pads under the tape, and new tape will eliminate it. Total cost: <$100. Time: <:30 minutes.

All the above are great ideas...but remember...it does take some getting used to. As your distances get longer you will build the necessary musculature to ride more comfortably. You can fix all the above stuff and still will have some discomfort.
I've found that good position, good gloves, frequent hand shifting, a good gel wrap are starts...a good lifting program that works the upper body well, including the hands and forearms is a plus.
Even folks who ride REALLY far, train for it and for whom 500 miles or more is "easy" have numbness from time to time.

I know my bike is fitted for me because I was sized before I bought my bike. Then, when I had the bike mechanic put it together he had all my measurements from my fitting. I wouldn't be surprised if I was putting too much weight on my hands. I guess I should work on my abs to support me more. If that doesn't work I'll try new gloves too. Thanks for the help!

Do a search here for some other threads on "ulnar nerve".

Here's what I did after hand numbness/pain became unbearable. Sorry if this repeats other's thoughts:
Bought gloves with good padding (Specialized even makes a special glove for this problem.)
Bought bar tape with gel pad underneath (also Specialized).
Bought Bontrager buzz-kill bar end plugs to dampen vibrations.
Got new bike fit to take weight off of the hands (more upright position). Slouching can also be a problem, whether on the bike or at the desk, as it impinges the nerve where it comes through the front of the shoulder/armpit and down the arm.
Bought a back support for my office work chair to force me to sit upright.
Received some deep tissue massage on the area.

(the great Graham Obree)

You guys just crack me up after a bad day at work thanx!

I have realized over the last year that the less padding i have down there the less soreness.
So i usually just train in tri shorts now. I have no ass by the way you would think i would
need all the extra padding but less seems to work better all around.

+1 to ht001. I still don't exactly have washboard abs, but I found that cycling became far more comfortable ("down there" issues aside) once my stomach and back muscles were stronger and therefore able to support more of my weight. In the interim, use all the equipment suggested. And, don't be afraid to stretch -- sit up on your bike to stretch your back and take the weight off your arms for a little bit, take a hand off the handlebars and flex your hand, wiggle your fingers.