It depends on what you are changing from and to. If you are changing from a barrier method to the pill, or the reverse, you may experience some side effects from the changes in hormone levels. Even from pill to pill, you may experience some mood swings or changes in your cycle. If you experience significant symptoms in mood, flow or other unusual symptoms, call your health care provider.
Always use a backup method such as condoms when you are changing birth control methods just to be safe.