When to avoid using a breadboard
Areas where the common breadboard does poorly:


High voltage
High frequency (above 10MHz)
Where the additional breadboard capacitance would present problems (oscillators, etc)
Where glitches due to poor wire connections would result in poor operation
Where most of the parts are not through hole 0.1" (2.54mm) centers
For anything but on-the-bench prototyping (ie, don't take it out of the lab and expect it to work)
Sensitive analog electronics, such as sensor usage