This is a very broad question and I would much prefer to look at specific examples. However, generally speaking, most supplements are safe to be taken together. There are some theoretical interactions that involve taking too many herbal/vitamin supplements that cause potential thinning of the blood. These include a list of about 150 different items but some of the most well recognized ones are Ginkgo biloba, CoQ10, Fish Oil, Vitamin E, Turmeric and Nattokinase. When taken together there is some theoretical risk of bleeding problems however in a healthy person on no medication and with no other bleeding risk factors there should be no problems.
Most issues with vitamins and herbs are related to their interactions with medications. If you take the above scenario and add prescription blood thinning therapy from something like Warfarin/Coumadin or Plavix it is a much more dangerous scenario. Even over the counter aspirin therapy can greatly potentate the interactions of herbs and vitamins.
Depression medications are another red flag for some herbal and vitamin supplements like St. John’sWort, 5-HTP and SAMe. It is best to discuss these issues with a qualified Naturopathic Physician before starting anything new.