Conversations in the Oval Office are generally not recorded. However, notetakers may be present in important meetings, especially those with foreign leaders.
Presidents could choose to bug themselves if they like, but as Richard Nixon demonstrated for the ages, it’s not such a good idea. No one is infalliable. A complete record of every utterance of even the most virtuous president is bound to include something unflattering.
It also might have a chilling effect on the level of candor with which aides offer advice. Knowledge that their words are being recorded might cause a president’s advisors pause about offering advice the president might not want history to hear. The ability of a president’s staff to speak frankly is critical. When presidents are wrong, and they sometimes are, aides need to be able to tell them that without fear of tarnishing their legacy.
Originally posted as an answer on Quora.