I know that in Harry Potter it was said that the PM was notified of Sirius Black's escape. Was he the only muggle in authority to know about the wizarding world? What about the President of the USA or other World Leaders?
In Britain, most likely the PM was the only official.
He is certainly the only one mentioned specifically, but it seems highly likely that wizards in other countries would have a similar protocol. We know that other countries have their own Ministries of Magic, and it only makes sense that the rules for contacting Muggle leaders should be consistent. (The President in he U.S.A would be kept informed similarly for example)
The books only mention the British PM because the books and events take place in Britain, but of course, there are wizards all over the world.
The primary reason for contact between the Minister for magic and the PM was to keep the Muggle PM informed of events that could cause alarm or notice in the Muggle world. Examples: the escape of Sirius Black, the rise of Voldemort, transporting dragons into the country for the Triwizard Tournament.
These types of things likely happen all over the world, so again, similar protocols must be in place.
I would bet, however, that none of the Muggle Leaders is ever told that the other Muggle leaders are aware of wizards. It would help to maintain the secrecy if the Muggle leaders were afraid to talk about contacts from Wizards amongst other Muggle leaders.
I know it's not canon, but the HP Lexicon, which is a bit more reliable than other sources also contains the following statement in the Ministry of Magic page:
The Muggle Prime Minister is aware of the wizarding world (HBP1) . Presumably this is also true of the President of the United States and of other world leaders.
The answer is right there in that chapter (chapter 1 of HBP). Here, the Prime Minister remembers what Fudge has told him the first time they've met:
‘The Minister for Magic only reveals him or herself to the Muggle Prime Minister of the day,’ […] ‘We find it the best way to maintain secrecy.’
This might of course apply only to the British Minister for Magic, with similar arrangements in some other countries.
The books only mention him, so it is highly likely that he is in fact the only one to know. I think that the wizards would avoid telling him, but feel it necessary for some reason (maybe to help cover up any mess?)The reason they may also avoid telling anyone else is that Muggles may begin to try and interfere, but with only one man, he will likely be to shocked/afraid to really do anything about it.
In addition to the current people in power, which the other answerers have covered, there is some debate among fans based on evidence from the Wizarding World of Harry Potter and some clues on JK Rowling's website about whether any members of the royal family are witches, wizards, or squibs; certainly a portrait of Bloody Mary appears in the films but that could just be random set dressing. See the Harry Potter Wiki for more information on this, the Anne Bolyen and Queen Mary I entries are the most relevant ones. Mary II certainly knew about them (according to the information from the WOMBAT exam on JKR's site). All of these examples are, of course, several hundred years old and from before the International Statute of Secrecy was enacted, so it's hard to tell how much these various royals knew and how much they dismissed as superstition, as Mary II's failure to send a delegation to the newly created Ministry of Magic could imply.
More information on historical relations between wizards and muggles-- particularly muggles of rank and power, such as royalty-- can be found in the Statute of Secrecy entry.
Considering that there likely are a lot of muggles knowing about the wizarding world, because some of their relatives are wizards or witches (e.g. the Dursley's, Hermione's parents, etc.) It doesn't seem too unlikely that some of these people are "people in authority". This is (well-founded?) speculation though, and the only person we are explicitly told is informed about the existence of magic is the British PM, as mentioned in several of the other answers.