No, with the computer unplugged from the wall outlet, there is no risk of yourself getting electricuted from a computer. However us humans carry static electricity, for example remember rubbing a balloon on your shirt and it sticks to a wall, or rubbing your feet on a carpet (in winter when it's dry) then touching someone and you give them a little shock? This is what I'm speaking of. If you have a little tiny buildup of a static charge in your body and you touch say a memory chip, zap, forget about your computer ever working again. Depending on what component you touch the discharge takes the closest route to ground and would damage anything succeptible. If you had a static charge in you and say when to wipe off some dust on the hard drive and touched a chip, that could erase or damgae your hard drive making it useless. It's unpredictable really.
Now when I spoke of grounding yourself, I simply mean touching something metal that is grounded. Touch the metal frame of the computer while its still plugged in. There is a ground wire that is connected to the metal frame that goes to the wall outlet and if the outlet is proper it should have an electrical ground, you know that 3rd middle leg on a plug. A radiator, desk something that would discharge any static charge built up in you.
Here is a better description:
Static Electricity and Computers
Whenever the casing of a computer is opened and its internal workings are exposed (to change a hard drive or add memory chips, for example), there is a danger of damaging the computer with the buildup of static electricity that is held by the human body. The internal workings of a computer, and especially the hard drive, are extremely susceptible to static electricity, which can cause considerable damage to the hard drive if it is zapped with even a small amount. Microchip damage can occur if it is exposed to static electricity as low as 500 volts, and humans are not able to perceive static electricity until it has reached about 1,500 volts. (Walking across a rug can produce a static electricity voltage of up to 12,000 volts, but static voltage is not life threatening.) So it is possible to damage a hard drive with static electricity that is not even felt by the person because it is at such a low voltage.
Static electricity is caused by a process called triboelectrification. Everything around us, and including us, is made of atoms, and every atom has in its center (nucleus) positively charged protons and neutrons, which have no electrical charge. Surrounding the atom are negatively charged electrons. The protons and neutrons in an atom do not change, but the electrons can move from one atom to another. When two objects touch, they exchange electrons, which causes one object to become electrically positive and the other to become electrically negative. When an object touches another object with either an opposite or neutral charge, electrons flow. Static electricity is created when electrons move back and forth between atoms.
To avoid zapping your components with static electricity, take precautions to ground the static electricity before touching any of the internal components of the computer. Wearing an ESD wrist strap will prevent any static electricity from damaging your computer. Another way to ground the static electricity is to touch the internal metal frame of the computer's case while the computer is plugged into an electrical socket. The static electricity will be discharged and grounded as the electrical circuit is grounded via the AC outlet. And to be on the safe side, always handle the electronic circuitry on the motherboard, video card, modem, sound card, hard drive and other internal components by any insulated, non-circuitry areas if they have them to insure that you do not send a bolt of static electricity coursing through it. http://www.webopedia.com/DidYouKnow/Com ... static.asp
Here is a links describing Static Electriciy in more detail: http://www.sciencemadesimple.com/static.html