If smoke comes out of your computer, it is most likely caused by the failure of the power supply. If this is the case, the computer will just stop and lose power. There is a cooling fan inside and the motors eventually wear out. Unplug the computer from power immediately to prevent possible damage to the hard drive (all your data is here), or other components. If it is the power supply, a new one can be purchased to replace the old one and you can get back to work.
If the smoke is coming out of your monitor, turn off and unplug your PC and monitor. Smoke should not come from your monitor unless you have configured it to operate outside its design parameters, such as the display frequency. If your monitor smokes, plan on buying a new monitor.
Another cause could be a short in one of the internal wires. If this happens, it is possible for their to be a small fire. Plan on a new computer if this happens.