It might be helpful to note that in the US, the fat ground conductor at the plug is connected by your house wiring all the way back to the ground connection at your circuit breaker box. The neutral connector at the plug (the wider of the two flat prongs) is also connected by your house wiring all the way back to the ground connection at the circuit breaker box. That's right - neutral and ground wiring are both grounded.
This is pretty important, because it is possible for a dangerous situation to occur when neutral is not correctly referenced to ground. A few years ago, I started to see some lights dimming and others brightening when some heavy electrical loads came on (refrigerator, freezer, etc). Initially I thought it was a problem with the power company's transformer, but it turns out that the clamp in my electrical entrance that connected the neutral leg to the local ground had loosened and when loads on one hot leg came on, they shifted the neutral's potential relative to ground and put more voltage on the opposite hot leg. Just a few minutes with a screwdriver and the problem was fixed - after a couple of weeks of head-scratching, getting visits from the power company, etc.
There are appliances, etc, that have polarized plugs on them. In other words, there are just the two flat prongs and no ground prong. There is only one way that plug will fit in the socket, since the neutral prong is too wide to fit the "hot" socket. This way, products can be designed so the on/off switch interrupts the hot wire so that no other part of the circuit beyond the switch can be energized. If you ever have to replace such a polarized plug, you must observe that polarity.
Safety tip:
If you have never checked the outlets in your house, do not assume that they are all wired correctly. Just go to the hardware store and for a couple of bucks you can buy an outlet tester. This is especially important if your house or apartment has been "modified" by a do-it-yourselfer in the past.