You are probably asking the question because you haven't gotten to alternating currents yet. One typical and simple example I can think of is the AC-DC War, AC won because it uses very high voltage and very low amperage to transmit electricity, this leads to very low power loss, compared to DC transmission. Although I have heard extremely high DC transmission lines are more efficient, but I haven't looked into it.
From what I understand (And I could be wrong) both amperage and voltage can be hazardous, but it depends. Another factor to take into account is, at very high frequencies, high voltages have no effect on humans because there is no time for the current to sink under your skin and reach your heart. So a tesla coil will transmit intesely high voltages but are not harmful to human beings at all (Picture of the kid touching the ball with rising hair comes to mind).
Voltage is needed for transmission of the current, amperage is generally what will do the damage though. Human beings have a resistance of 10,000 Ohms, at 120V this equates to 12mA. You would need about 25-30mA to cause shock to your heart. At higher voltages I would assume it becomes more and more dangerous as the amperage through your body increases.
But just so you know I am only a second year undergraduate physics major, so hopefully this answer holds you over until someone smarter can answer you correctly.
Also, you can go to this site:
If you look for the circuit construction kit, you can use the applet to find out how circuits work.