Generally, distilled water is not dangerous. Distilled water is water that's been purified through boiling. Any impurities in the water, whether they boil off at a lower temperature or stay behind after the water evaporates, are removed, often via a charcoal filter. These impurities may be chemicals, pathogens or both.
Problems may arise because "normal" drinking water contains minerals that are needed by the body, such as calcium and magnesium. A person who is deficient in these minerals should be careful when drinking only distilled water. Some medical experts believe that distilled water actually pulls electrolytes and vital minerals from the body.
Also, though store-bought distilled water is potable, water that is collected from other places might not be safe to drink even if it is distilled. Water can be so polluted that normal distillation doesn't rid it of all toxins.
When distilling water, ensure that the equipment is clean, because contaminants can get into the water even as it is being distilled. This is especially important if the water is being distilled at home. The vessel that the water is collected in might also be of concern. It must be clean, and some plastics actually leach into the water and contaminate it.