There are various levels.....
ACGME controls & regulates residencies. Residencies are financially payed for by Medicare. To practice (and this is law, though I don't know if its a federal or state law) you need to pass USMLE 1, 2 and 3, and graduated from an accredited residency program, need a medical license to practice in the state, and have malpractice insurance.
While practicing in the state, the state medical board is in charge of doctors. The board can take away a doctor's license.
Who regulates psychiatry? The American Board of Psychiatry and Neurology gives board certification, though certification is not required to practice.