After resistor's value, maximum applied voltage, power dissipation is the next most important characteristic of a resistor. An overloaded resistor often changes in value over time and can often get hot enough to burn itself and surrounding components. Every circuit designer learns the smell of burnt resistor sooner or later!
The common rule of thumb is to calculate how much power the resistor will have to dissipate and then use the next largest size or a factor of two higher dissipation rating, whichever is larger. The power rating is based on unobstructed air circulation around the resistor. For resistors dissipating more than a watt, arrange nearby components so that air can circulate freely. If possible, mount power resistors horizontally so that convection cools all parts of the resistor equally.