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The answer will be different if you refer to general harmonic distortions of signals Distortion - Wikipedia, the free encyclopedia, electrical energy or radio frequency applications. Generally, I doubt that they are dangerous.
Any system (or an object) set into vibration / oscillations has its own natural frequency. In addition to its natural frequency it has tendency to vibrate at higher and lower frequencies as well, of course to a lower extent. If the natural frequency is F say, it vibrates at frequencies 2F 3F etc. These are higher harmonic frequencies of oscillations present with relatively loer amplitudes. What is dangerous depends on given situation and criterian.
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