There have been several monarchs throughout history who, although they actually ascended the throne and were the monarch, had their reigns cut short. Some extremely short. Some died, some abdicated, some were deposed. But, for however short a period, they reigned.
Our modern “enlightened” historians, however, have decided to take it upon themselves to take offense at the short lengths of some reigns, and absurdly declare that the monarch “never reigned”, which is absolute baloney (I’m being polite here). And despite the lunacy of their approach, it is the one adopted by the majority of conventional historians. And thus, while ALL of the persons on this list reigned, you will rarely – if ever – find them in “official” lists.
Edgar II (c. 1051-c.1126)
Known as “Edgar Ætheling”, Edgar II was proclaimed King of England on the 15th of October, 1066, following the death of Harold II the previous day in the Battle of Hastings. On his father’s side, he was the grandson of King Edmund II (“Ironside”). However, William II, Duke of Normandy (now known as “William the Conqueror”), having defeated and killed Harold at Hastings, was now advancing across the English countryside. New king Edgar’s attempted resistance was futile, and Edgar abdicated the throne to William on December 10th, and William officially ascended the throne on December 25th as William I. 
Yes, there was a King of England named Eustace. He was the son of King Stephen and his wife Matilda I, Countess of Boulogne. He inherited his mother’s position as Eustace IV, Count of Boulogne. His father appointed him the co-King on 6 April 1152 as a means of ensuring succession. King Eustace died suddenly the next year on the 17th of August, 1153.
King John was hugely unpopular, and in 1215 the First Barons’ War broke out. In 1216, the barons invited the French heir-apparent, Louis, to become King of England. Louis was a cousin of John’s, and married to John’s niece. Louis landed unopposed in Kent, England, in 1216. He soon conquered more than half of the country – including London – and was triumphantly paraded in the city as the King of England, where he was enthusiastically greeted by the commoners. However, King Louis’ fortunes soon turned when John (who was still king of about half the country) died in October. Many of the barons immediately switched loyalties to John’s son Henry III. King Louis began losing the war to King Henry III’s forces (who took orders from my ancestor William Marshal, 1st Earl of Pembroke, who served as young Henry’s regent; I also descend from King John and Lady Matilda). Louis’ reign ended on 22 September 1217 when he signed the Treaty of Lambeth, acknowledging that his reign had not been legitimate. He later became King Louis VIII of France.
You’ve probably heard of her; England’s second female monarch, and the first to be Queen. The dying teenager Edward VI appointed his cousin Lady Jane Grey as his successor. Edward died on July 6th, 1553. While his death was initially kept quiet, Jane was proclaimed the Queen of England on the 10th. Her Catholic cousin Princess Mary – elder half-sister of Edward VI – gathered enough popular support to overthrow the Queen on July 19th, hence Queen Jane’s nickname “The Nine Day Queen”. Princess Mary succeeded her as Mary I.
James VIII (1688-1766)
The only legitimate son of the exiled James VII (II of England and Ireland), James Francis Edward Stuart claimed the English, Irish and Scottish thrones as “James III and VIII”. For the most part, he was a pretender. However, he was briefly the actual King of Scotland. In 1715, he launched an invasion of Great Britain, intending to take the throne. By October, his forces had successfully taken Scotland, and he was now the de facto King James VIII. By early 1716, however, the battle had turned on James’ supporters, known as the Jacobites, and James VIII effectively abdicated the Scottish throne on the 4th of February, thus ending one of the shortest reigns in Scottish history.
However, that was not the last heard of him. In mid-1745, James’ son, Charles Edward Stuart, launched an invasion of Scotland in a bid to place his father on the throne again (with Charles as regent). On the 17th of September, Scotland’s capital, Edinburgh, fell to the Jacobites, and James VIII was once again declared Scotland’s sovereign, and his son Charles declared Prince Regent. This time, however, even more of Scotland was under James’ sovereignty. By the 16th of April, however, the Jacobites had been soundly defeated, and James was no longer King, and Charles no longer Regent. The Jacobites never again attempted to forcefully regain the throne.
Henry II (1421-1471)
King Henry V of England, in order to end the ongoing war with France, married King Charles VI of France’s daughter Catherine of Valois. They made a treaty by which Henry V and his heirs were Charles VI’s heirs. They had a son, Henry, Prince of Wales, in 1421, who thus became the heir apparent to the English throne, and 2nd-in-line to the French one. Shortly afterwards, Henry V died, and Prince Henry became King Henry VI (and the heir-apparent to the French throne). A couple of months later, Charles VI died, and Henry VI of England was now King Henry II of France. However, many French were angry about this nicknaming Charles VI “the Mad”. Charles’ son was quickly proclaimed King Charles VII by some Frenchmen. England controlled the northern half of France, while the French controlled the southern half. Each half had a different King – Henry II in the north, Charles VII in the south – and both claimed the entire country. Finally, in 1453, Charles VII’s forces (under Joan of Arc’s command) won back almost all of France, apart from Calais, thus ending Henry II’s reign as King of France (although he continued to reign as King of England as Henry VI). Henry II’s French reign ended on 19 October 1453, having begun on 21 October 1422 (his English reign having begun on the 31st of August that year). Not only has he gone unacknowledged as an actual French monarch, the next King Henry of France took on the name of Henry II, even though he was Henry III. All subsequent French kings Henry are therefore misnumbered.
Napoleon II (1811-1832)
France’s famous Emperor Napoleon I (aka Napoleon Bonaparte) abdicated as Emperor of the French on 4th April 1814 in favour of his 3-year-old son, Napoleon François Joseph Charles Bonaparte, who automatically became Emperor Napoleon II. Two days later, however, on the 6th, Napoleon fully abdicated in favour of his son as well as himself, thus ending Napoleon II’s two-day reign.
However, a year later, Napoleon was out of exile and the Emperor of France again. After his defeat at the Battle of Waterloo, Napoleon I once again abdicated in favour of his son on June 22, with Napoleon automatically gaining the Emperorship again. 4 days later, on the 26th, the French government deposed Napoleon II. Almost two weeks’ later, his father’s predecessor (and successor) Louis XVIII officially became King on 8 July, and some count Napoleon II’s reign as having ended on the 7th of July. Either way, he was monarch, and is idiotically denied by modern historians.
Louis XIX (1775-1844)
King Charles X faced a revolution in 1830, and was forced to abdicate. On the day of his abdication – August 2nd, 1830 – the revolutionaries sat down Charles and his surviving son, Louis, and presented them with documents abdicating the throne and/or a claim to the throne. Charles X signed, thus automatically making his son King Louis XIX. Just under 20 minutes later, Louis (who for those 20 minutes listened to his wife’s pleas not to abdicate) signed his document, thus ending the shortest reign in history.  
Henry V (1820-1883)
When Louis XIX abdicated, he abdicated in favour of his 10-year-old nephew, Henry, Duke of Bordeaux, who automatically became King Henry V (or Henri V in French). (He was actually Henry VI, but as explained above, the original Henry II goes unacknowledged.) A week later – August 9th – the French government deposed Henry V and replaced him with his distant cousin Louis Philippe, who became King Louis Philippe I.
Louis Philippe II (1838-1894)
19th century France certainly didn’t like acknowledging its monarchs, did it? In 1848, King Louis Philippe (I) was forced to abdicate. Louis Philippe did so on the 24th of February, and his 10-year-old grandson Philippe, Count of Paris, automatically became King Louis Philippe II. However, just 2 days into his reign, on the 26th, the French National Assembly abolished the monarchy and declared the Second Republic. Louis Philippe II was thus the last King (and second-to-last monarch, the last being Emperor Napoleon III).
Alexei II (born 1904)
Czar Nicholas II was forced to abdicate on 15 March 1917, due to the Revolution. He abdicated in favour of his son, who automatically became Czar Alexei II. A few hours later, due to the advice of doctors over Alexei’s medical condition, Nicholas abdicated again, this time for his son (although its legality is debatable). 
Michael II (1878-1918)
When the former Czar Nicholas II abdicated for his son Alexei II, his (Nicholas’) brother Grand Duke Michael automatically became Czar Michael II. Michael didn’t find out he was Emperor until the next day. Some military units had already taken an oath of allegiance to him. However, he signed a document that proclaimed he would accept the throne if the people wished it; he neither accepted nor abdicated the throne. Some therefore view his reign as having ended on 16 March 1917 – reigning for less than a day – while others view his reign as laughing until his murder on 13 June 1918, for just over a year. Either way, he reigned.
Victoria Kamāmalu (1838-1866)
As both a crown princess and Kuhina Nui, she was technically head of state (Queen) between the death of her brother Kamehameha IV at 9:15 AM, November 30th, 1964, until her brother Kamehameha V’s ascension to the throne at 3:00 PM that day.
Upon the death of Emperor Xiaoming on 1 April 528, his mother Empress Dowager Hu immediately put his infant daughter on the throne, Hu having falsely declared her granddaughter as a son. Less than 5 hours later, however, she deposed her granddaughter and replaced her with Yuan Zhao.
Liu He (c.92BC-59BC)
Liu He was installed as the Emperor of China on 18 July 74 BC, but deposed less than a month later on August 14th. He was enthroned by his regent, and subsequently deposed by him, subsequently becoming Marquis of Haihun. Despite reigning, he was omitted from the official list of emperors.
Following the death (probably poisoning) of Emperor Zhongzong, his wife Wei placed his son Li Chongmao on the throne, hoping to control the youth (she was probably behind her husband’s poisoning). She was wrong, and deposed him 17 days later. He died 4 years later and was given the posthumous name “Emperor Shang”. Traditional historians did not count him as an emperor (even though he was), although modern historians usually do. He reigned from 8-25 July 710.
Installed as the successor of Emperor An, the young emperor Liu Yi was deposed very shortly afterwards and murdered the next year.
Luís II (1887-1908)
King Carlos I was murdered in a shooting spree on 1 February 1908, and his eldest son Luís died 20 minutes later, thus technically making him King Luís II for 20 minutes (rivaling Louis XIX of France for the title of shortest reigning monarch of all time).
Mindaugas II (1864-1928)
Towards the end of World War I, on 16 February 1918, the Kingdom of Lithuania declared its independence from the German Empire. On 11 July 1918, Wilhelm Karl, Duke of Urach, was elected King of Lithuania. He took on the name of Mindaugas II. However, due to Germany erupting into civil war, the Council of Lithuania suspended Mindaugas II’s kingship on 2 November 1918 – before Mindaugas even arrived in Lithuania!
There are, in probability, more denied monarchs than I have documented. And I’m not counting the historical monarchs who are now labelled “legendary” or “mythical”, like King Arthur. But these are enough.