Everything Kellenjb has told you is absolutely true. What I would like to add is some further information on how do deal with this issue when building electronic circuits.
You have two pieces of gear involved, a power supply and the circuit under test. Now clearly if the circuit under test tries to draw too much power, and the power supply is not able to safely deal with it, then bad things (like a fire) can happen.
Consider what happens when there is a bug in the circuit under test and it draws excessive power from a supply (like a car battery) that is capable of providing lots of power safely. In this case it is not the supply that is the problem but rather the circuit under test that might catch fire, or more likely release it's "magic smoke".
The way this is generally dealt with in a lab where prototypes are built is to use a bench power supply that can be current limited. It will generally have two displays (meters or LEDs etc) on the front, one for voltage and one for current. It will also have a way to set both the desired voltage and or current. It will operate in either a voltage limited or current limited mode.
Now suppose you put together a circuit on a breadboard and you compute that it will require 5 V and use a maximum or 100 mA. You would put those values into your bench power supply which would guarantee that the voltage would never exceed 5 V (it could be less if you short the terminals) and that no more than 100mA of current will be delivered. If your circuit attempts to draw too much power the power supply will give an error indication and prevent excessive current from flowing.
While such a supply can not guarantee that the components in your circuit will never be damaged (you could wire the leads up backwards for example), they can greatly reduce the chances of destroying a component and perhaps more importantly prevent a fire.