That is bad -
Dryer usually runs on 208/240 voltage so it is across the two "line" rails
if you have a 3 wire plug, 2 pins are "hot" and the 3rd is neutral
if you have a 4 wire plug , 2 pins are "hot", the 3rd is neutral and the 4th is ground
On a 3 wire plug the neutral is usually connected to the frame of the dryer

For it to shock you, you had to complete a circuit, so part of you must have been touching something else as well

SO
get a meter ( places like harbor freight have them cheap) set the meter on the 250 volt scale
and touch one lead to the case and the other to a nearby water pipe,
If you see a voltage more than a few volts, you do have a problem.
if the meter read near 120V, either your dryer, the outlet, or the breaker/fuse box is wired wrong.
if the meter reads some voltage ( more than about 2V) then you have a significant ground loop
or improper ground bonding in your breaker or fuse box

Unplug the dryer, change meter to continuity setting, touch the frame with one lead and the "L"
or "O" shaped plug pin, the meter should beep, if not, your dryer has a connection problem.
Now touch either of the flat pins, the meter should not beep.
If it beeps, your dryer has a serious short, discontinue use and call an electrician.

I can tell you more things to test, but I would need to know how good you are with electricity first.
If you are in the baltimore MD area, let me know

First of all, I'd kill power and check continuity between
the bare wire and a known ground source, such as the
grounding buss in the breaker panel. There should be
virtually no resistance. It could be a double problem,
with an open ground being one but my instinct is that you
have an element shorting to the water. It'd produce enough
voltage to buzz you, but it might not be enough to trip the
breaker.

The other thing I'd check is the water heater. I'd check
each leg to the water heater's ground. There should be
infinite resistance, as in "open." Personally, I bet that
at least one leg shows some resistance, telling me that an
element is shorting to the water.

If it was my house, I'd take the time to simply rebuild the
electric heater.

First of all, drain it well and get any crud out of it.
Remove both elements and replace them with the low
temperature ones. They are the wavey ones and will last a
lot longer- especially in harder water. While you're at it,
I'd replace both the upper and lower thermostats. When
you've done that, you essentially have a new electric heater.

Nonnymus

I assume this was a reply to my water heater shock issue. Can you
elaborate on checking "each leg"? I am pretty handy but a pure novice
when it comes to electrical issues. The unit is 9 years old, perhaps a
new water heater is in order!

Nonnymus wrote:
First of all, I'd kill power and check continuity between
the bare wire and a known ground source, such as the
grounding buss in the breaker panel. There should be
virtually no resistance. It could be a double problem,
with an open ground being one but my instinct is that you
have an element shorting to the water. It'd produce enough
voltage to buzz you, but it might not be enough to trip the
breaker.

The other thing I'd check is the water heater. I'd check
each leg to the water heater's ground. There should be
infinite resistance, as in "open." Personally, I bet that
at least one leg shows some resistance, telling me that an
element is shorting to the water.

If it was my house, I'd take the time to simply rebuild the
electric heater.

First of all, drain it well and get any crud out of it.
Remove both elements and replace them with the low
temperature ones. They are the wavey ones and will last a
lot longer- especially in harder water. While you're at it,
I'd replace both the upper and lower thermostats. When
you've done that, you essentially have a new electric heater.

Nonnymus