Putting too much anti-freeze in your car at once is bad for various reasons. Many people put too much anti-freeze in their car. You can usually get away with it if your car is a newer version, you have a new radiator or hoses, and/or you haven't done this more than once or twice.
To put it simply Anti-freeze prevents your car's radiator from freezing in cold weather, and cools your car at the same time. Most brands of anti-freeze are made with ethylene glycol. The problem starts when you start up your car the next morning, the anti-freeze prevented the water in the radiator from freezing overnight.
Now unfortunately, as the car heats up, the coolant gets hotter, and when things get hotter they expand. When this happens a few other things happen. First, depending on how much you overfilled it, the various hoses going to the components (transmission, engine, oil, etc) of your car may start to leak because of the pressure. This is a problem because it will cause major damage to both your hoses and the internal pipes of the radiator itself.
Second, the anti-freeze will start to come up and leak out of the cap. This is an issue because the hot anti-freeze can melt some of you car's components. Hot anti-freeze can do damage to the underside of the hood, the battery casing and any wires or plastic tubes. Once you step into your car there will most likely be a warning light that signals you have a problem, if you are driving almost any modern car. If you do happen to overfill your anti-freeze, then don't worry immediately. In many radiators there is a automatic pressure release device that will release some of the anti-freeze if the pressure reaches a high level.
In most cases having too much anti-freeze will not overheat or damage your car's internal areas. If you are noticing temperature changes or a continuation of the warning light flashing on your dash a few days after overfilling, then you may want a diagnosis done by your mechanic, as it may have clogged some tubes or may have done damage to the radiator itself.
Usually you shouldn't have to be worried about overfilling anti-freeze the first or second time, but you will want to keep an eye out for changes. If you overfill you anti-freeze be sure to have extra in the trunk in case something does start leaking, and it needs immediate attention. Lastly, make sure you wait at least an hour before opening the cap to the anti-freeze or you will be splattered with hot coolant. Be safe!