So help me God is a phrase often used to give an oath, and most commonly optional as part of an oath of office. It is also used in some jurisdictions as a form of oath for other forms of public duty, such as an appearance in court, service as a juror, etc.
The essence of the phrase is to emphasize that one means what one is saying or has said. It therefore implies greater care than usual in the act of the performance of one's duty, such as in testimony to the facts of the matter in a court of law.
The use of the phrase implies a greater degree of seriousness and obligation than is usually assigned to common conversation. See the discussion on oaths for more details.
In Canada, the Oath of Office, Oath of Allegiance, and Oath of Members of the Privy Council may be sworn, and end in "So help me God." They may also be solemnly affirmed, and in such case the phrase is omitted.
In 2009, concerns about the phrase infringing on Constitution of Croatia were raised. Constitutional Court of Croatia ruled them out in 2017, claiming that it is compatible with constitution and secular state. The court said the phrase is in neither direct nor indirect relation to any religious beliefs of the elected president. It doesn't represent a theist or religious belief and does not stop the president in any way from expressing any other religious belief. Saying the phrase while taking the presidential oath does not force a certain belief on the President and does not infringe on their religious freedoms.
The Constitution of Fiji, Chapter 17 requires this phrase for the oath of allegiance, and before service to the republic from the President's office or Vice-President's office, a ministerial position, or a judicial position.
In New Zealand the Oath of Allegiance is available in English or Maori in two forms, one an oath containing the phrase 'so help me God' and the other an affirmation which does not. The Police Act 1958 and the Oaths Modernisation Bill still includes the phrase.
In the Oath of Office of the President of the Philippines, the phrase "So help me God" (Filipino: Kasihan nawâ ako ng Diyos) is mandatory, though the phrase can be omitted voluntarily, in which case it would become an affirmation instead of an oath. An affirmation, however, has exactly the same legal effect as an oath.
In the United States, the No Religious Test Clause requires that "no religious test shall ever be required as a qualification to any office or public trust under the United States." Regardless of that, there are federal oaths which do include the phrase "So help me God", such as for justices and judges in 28 U.S.C. § 453.
The phrase "So help me God" is prescribed in oaths as early as the Judiciary Act of 1789, for U.S. officers other than the President. The act makes the semantic distinction between an affirmation and an oath. The oath, religious in essence, includes the phrase "so help me God" and "[I] swear". The affirmation uses "[I] affirm". Both serve the same purpose and are described as one (i.e. "... solemnly swear, or affirm, that ...") 
There is no law that requires Presidents to use a Bible or to add the words "So help me God" at the end of the oath. Historian John R. Alden maintains that George Washington himself added the phrase to the end after administration of his first oath. However, all Presidents since Franklin D. Roosevelt have used this phrase, according to Marvin Pinkert, executive director of the National Archives Experience.
The United States Oath of Citizenship (officially referred to as the "Oath of Allegiance", 8 C.F.R. Part 337 (2008)), taken by all immigrants who wish to become United States citizens, includes the phrase "so help me God"; however 8 C.F.R. 337.1 provides that the phrase is optional.
The Enlistment oath and officer's Oath of Office both contain this phrase. Normally, it is not required to be said if the speaker has a personal or moral objection, as is true of all oaths administered by the United States government. However, a change in October 2013 to Air Force Instruction 36-2606 made it mandatory to include the phrase during Air Force enlistments/reenlistments. This change has made the instruction "consistent with the language mandated in 10 USC 502". The Air Force announced on September 17, 2014, that it revoked this previous policy change, allowing anyone to omit "so help me God" from the oath.
Some of the states have specified that the words "so help me God" were used in oath of office, and also required of jurors, witnesses in court, notaries public, and state employees. Where this is still the case, there is the possibility of a court challenge over eligibility, as the U.S. Supreme Court ruled in Torcaso v. Watkins, 367 U.S. 488 (1961), that such state-law requirements violate citizens' rights under the federal Constitution. Alabama, Connecticut, Delaware, Kentucky, Louisiana, Maine, Massachusetts, Mississippi, New Mexico, North Carolina, Texas, and Virginia still require "so help me God" as part of the oath to public office. Maryland and South Carolina did include it, but both have been successfully challenged in court. Other states, including New Hampshire, North Dakota, and Rhode Island, allow exceptions or optional phrases. In Wisconsin, the specific language of the oath has been repealed.