The nation crowning the woman king wants to make it clear that she rules in her own right rather than as consort.
The Queen is masculine, and the title of "King" denotes masculinity rather than the possession of Y chromosome.
The original title is gender-neutral when taken literally. It either carries a non-literal masculine connotation because males are more likely to bear it or is represented by a masculine term in translation because of gender assumptions on the part of the translator.
This was the concept behind one of the earliest filmed versions of Hamlet. Hamlet, played by Asta Nielson, is a girl being raised as a boy so that she will inherit the throne on her father's death. This repression is the source of much of the young prince's famous angst, besides the true reason why "he" rejects Ophelia. (In fact, Hamlet is in love with Horatio, who doesn't know the truth until it's too late to reciprocate).
In Mercedes Lackey's By the Sword, it's mentioned that the current Son of the Sun, leader of theocratic Karse, is a woman pretending to be a man, including wearing a faux mustache.
Discworld: Technically happens in Guards! Guards!, but only because nobody'd thought (or dared) to ask the dragon who'd seized temporary rulership of Ankh-Morpork if it was male or female before they started calling her "King".
Myth and Legend
The legendary Pope Joan, who, it was claimed, lived in the 9th century, disguised herself as a man and reigned as Pope "John" for a few years until she was exposed as a woman when she gave birth on horseback.
In Soul Calibur: Legends The Masked Emperor of the Holy Roman Empire is actually a woman, despite having a (granted, rather effeminate) male voice with the mask on. You'd think gendered pronouns would give it away, but she always refers to herself as we. It gets weird when she says things like, "Don't tell anyone that we are a woman."
Cartman: Don't ask why Kenny wanted to be a chick, it's just how he seems to be rolling right now.
In Fate/stay night, Saber is King Arturia Pendragon. She was pretending to be a male King Arthur, but according to the narrator, most people in her inner circle (besides Merlin and "Arthur"'s official wife, Guinevere, who both already knew) either realized or at least suspected that she is a girl, they just chose to ignore it.
Gender Flipped and Played With on South Park: during the Black Friday three-parter Kenny's character is a girl, though of course everyone knows he's really a boy. He insists on being called a "princess," but Cartman, not wanting to share authority with him, only allows him to take the title "Lady McCormick." This is at least part of the reason that he betrays the X-Box players for the PS 4 supporters. See above under "Video Games."
Examples of women with a masculine title
Anime & Manga
Various Ancient Belka Kings in Magical Girl Lyrical Nanoha still keep that title even if they are female. Specific examples are Sankt Kaiser Olivie Sägebrecht and Ixpellia, the king of Galea. And Lord Dearche is always referred as "king" by other people.
Nanoha and Fate's Devices call them "Master" and "Sir", respectively. Chrono's device uses the gender-neutral "boss". This was lampshaded as a Running Gag in The Abridged Series:
Bardiche: Yes, sir! Fate: That's "ma'am!"
Sir Integra Hellsing. Although this is most probably a mistake on the part of the author (the proper title for a woman of her stature being "Dame"), Fanon holds the explanation that she took a masculine title in order to assert her authority over the Hellsing organization.
Soldier #1: Hey, you do know that our CO's a woman as well...
Soldier #2: She's too scary to be a woman!
The Idol masters in Idolmaster: Xenoglossia are all girls. In the original game the idol 'master' was the player, a producer (master) of idols but because Sunrise made the anime In Name Only the 'masters' of the 'Idols' (giant robots in this instance) became female.
In High School D×D, this is more of a chess motif during a Rating Game. An example would be Rias herself who is considered a King because she's the most important person in that particular game.
Similarly the inverse is seen in some teams with male characters taking the "Queen" position.
Inverted in One Piece by the Queen of Kamabakka Kingdom, Emporio Ivankov... who is male. Most of the time. His Devil Fruit Powers enables him to control hormones, so he can turn into a she at will - but still spends most of his time as a cross-dressing guy (who is NOT likely to fool anyone), wearing the title of Queen.
Of course, it's a deliberate joke in this case - Kamabakka Kingdom apparently consists entirely of cross-dressing men, making Ivankov a DRAG-Queen.
In Hunter × Hunter, all 14 children of the King of Kakin are referred as "Princes", regardless of their gender, so everyone can be treated equally and have the same right to succeed the crown.
In A Brief History of Equestria this happens to Princess Platinum — as the only child of King Aurum in the patriarchal Kingdom of Unicorns, theoretically her father's death would have started a civil war among the members of the Deadly Decadent Court. To prevent this, Aurum exploited the Exact Words of the law, pointing out that "says that the queen cannot rule. Doesn’t say the King cannot be a mare," allowing Platinum to take the throne under the title of King.
Frostblood has Jaina as the new Lich King and often referred to as the Lady King. This is due to a nerubian queen who can't tell the difference between genders of other races and a troll's decision to combine her titles of Lady and King. Only once is it ever brought up that she should be the Lich Queen.
In Pirates of the Caribbean, the nine leaders of the pirates are called Pirate Lords, regardless of gender. And their leader is called the Pirate King, also regardless of gender, as demonstrated when Elizabeth Swann gets the dubious honor.
A variation of this trope in Beasts Of The Southern Wild wherein Wink insists that his daughter Hushpuppy is going to one day be "the king of the Bathtub." Not queen, king.
In the Heralds of Valdemar series, starting partway through the Mage Winds trilogy the High Priest of Vkandis and ruler of the theocracy of Karse is a woman named Solaris, whose title is "Son of the Sun". Having been handpicked very publicly for the position by Vkandis himself seems to have thoroughly overcome the gender barrier that previously existed with regards to the role, but the terminology remains unchanged.
Likewise, D'ol Falla in the Green-Sky Trilogy is High Priest of the Vine, and women who run guilds are called guild-masters.
Xanth has this In this case The King of Xanth is defined as its ruler (at least among the human inhabitants) while The Queen of Xanth is defined as the King's spouse. Turns out, they never explicitly defined the King as being male, that had just been assumed to be the case for centuries due to the requirement that the office (which is not hereditary) has to go to a Magician. Since females with powerful magic were called Sorceresses, it was believed that they didn't qualify. Until somebody pointed out that a Sorceress is defined as a female Magician, and thus is also a Magician.
Which not only paved the way for this trope, but for its inversion: a female King of Xanth's spouse is a male Queen.
Not that it necessarily would have been impossible to just change the rule, but in the book where they figured this out, they had to replace the king regularly and quickly until they could defeat the villain who kept putting the kings into enchanted sleep, some of the most qualified successors were female, and this way was less headache.
In Megan Whalen Turner's series The Queen's Thief, the Queen of Eddis is called Eddis when as a woman she should have been called Eddia.
In Tamora Pierce's Song of the Lioness series, the Lady Knight Alanna is referred to as "Sir Alanna." This is because she masqueraded as a boy for literally the entirety of her knight training because girls weren't allowed to become knights, and as a result was knighted as "Sir Alan" and only revealed to be female afterwards. As a result she does not carry a shield with a distaff (feminine) border. Keladry of Mindelan, on the other hand, is "Lady Knight Keladry" because she trained openly as a female, and has a distaff shield. (Word of God says that Alanna retained the "sir" to make a point, and that Kel uses "Lady" to make a different point.)
In Pyramids, there's precedent for the royal family of Djelibeybi being able to change sex by decree. "No, sire, she is a man. She herself declares this."
In Honor Harrington, only men of the royal line can be Emperor of the Anderman Empire. At least once an emperor failed to produce any male heirs and it looked like there would be a dynastic civil war between his various cousins. Then his sister proclaimed herself to be a man and took the throne, basically daring all her male cousins to object if they thought they could make it stick. They universally declined the offer and, by all accounts, she became one of the empire's longest ruling and most effective leaders since the original Gustav Anderman himself.
A borderline case (in that she's only the head of household rather than a monarch) occurs in the short story Obligated Service. An extended family has a lack of males with the legal head of household being an immature teenager (since on Grayson only men can be the head of a household). One of the female family members is made the official head of the household on the grounds that as a naval officer she is legally a Gentleman
In Temeraire, the Tswana society resolves around ancestor worship, and they practice telling stories of deceased loved ones to dragon eggs, so that the dragons are born as reincarnations of great leaders. This has led to their entire empire being led by a young female dragon who is the "reincarnation" of their last king.
In a later book (Crucible of Gold) we discover that the Inca Empire's human population has been so badly ravaged by European diseases that a woman currently holds the position of Sapa Inca due to attrition.
In The Enchanted Forest Chronicles, king and queen are unisex titles in dragon society, and apparently quite different in function. When Cimorene, a human princess from a typical medieval fairytale kingdom, asks female dragon Kazul why she takes the title of king rather than queen when she becomes the ruler of dragonkind, Kazul retorts that the perks and duties of the queen of dragons are much less desirable than those of the king.
In the Dragaera novels, members of aristocratic Houses are broadly referred to as "____lords" (Dragonlord, Dzurlord, etc) regardless of gender, and the Warlord may be of either sex. At least one inversion — the Lady of the Chairs, an official court office currently held by a male — is mentioned in Iorich. Averted with noble titles such as Duke, Count, or Empress, which do get adjusted for gender of their incumbent.
This is the whole basis of the book Ladylord. The ruling lord has only daughters, and so names one of them his "son". The title of the book is a reference to the odd style some people use due to her unique situation. Her political maleness doesn't extend to actually being considered male in other senses, however - she has a husband rather than a wife, for example.
In Star Trek up until Voyager female superior officers were called "Sir". Janeway refused that, insisting on being called Captain or "Ma'am". In spite of this, the bridge crew still called her "Sir" periodically.
Ronald Moore decided this was worthy of exporting to the rebooted Battlestar Galactica. Thus Lieutenant Starbuck, President Roslin, Admiral Cain, etc. are addressed as "Sir", although "Ma'am" remains in civilian usage. So President Roslin's aide Billy Keikeya addresses her as "Ma'am" and Captain Apollo addresses her as "Sir" because she's his commander-in-chief.
In the Doctor Who episode "The Next Doctor", Miss Hartigan is pronounced the CyberKing.
On Farscape, Zhaan refers to herself as a priest, not a priestess. Her native word for her job is "Pa'u", but she's rarely called anything other than just "Zhaan". Zhaan is actually a sentient plant, so it's unclear whether other characters are just assuming feminine gender based on appearance.
On Due South, Fraser habitually refers to his boss, Inspector Thatcher, as "sir".
In Hikari Sentai Maskman, Prince Igam is working with the bad guys in order to restore the Igam Clan to their former glory (and gets into friction with the others because her goals aren't always in line with her boss's.) She uses male pronouns. However, bizarrely, a number of characters are astonished when she is "revealed" to be female even though she did nothing to alter her obviously female features and voice.
Captain Gates, the replacement of Captain Montgomery, on Castle is a woman who insists on being called "sir".
On the reality show King Of The Nerds, winners are referred to as "King" regardless of gender. Both the winners of season 1 and 2 were female.
In "Moment 4 Life" by Nicki Minaj, she refers to herself as king and this is even shown in the music video, which has a Storybook Opening that starts with "Once upon a time, there was a king named Nicki."
In Traveller, among the Aslan on the rare occasions that there is no male heir for a male position it is known for females to be declared "legally male". She must swear celibacy and act as a male in all duties appropriate to her gender. According to canon, this is more common in Aslan legends than in practice.
"Prince" is the title for the vampire ruler of a Camarilla city in Vampire: The Masquerade or pretty much any city in Vampire: The Requiem, regardless of the prince's sex. The former explains the title as a tribute to Niccolò Machiavelli, as a Camarilla prince secures his/her position through cunning, charisma and brutality, not heredity.
In Masquerade, the Sabbat use a lot of titles from the hierarchy of the Catholic Church, although nothing stops women from holding any specific office. The rough equivalent of a Prince would be an Archbishop.
In the Tir Tairngire supplement for Shadowrun, all members of the nation's ruling council are called "Prince", regardless of gender. The female council members are the ones who insist upon this practice, as they believe "Princess" would convey too much of a frilly-Disney-eye-candy public image.
Inverted: Some references in Exalted suggest that whoever ascends to control of the Realm will continue the title of Scarlet Empress regardless of their own gender (although the tendency to assume that the new ruler will be an Empress may just be acknowledgement of the fact that most of the prime candidates are women).
Exalts are also called "Princes Of The Earth", regardless of gender. Same with Green Sun Princes.
In Planescape, this is the apparent case with Shemeshka the Marauder, a yugoloth who calls herself King of the Crosstrade, due to being the undisputed master of the largest network of spies, thieves, assassins and other unsavories in Sigil, and who flies into an infamouse rage if the matter of her technically being the Queen of the Crosstrade is brought up. According to the "Uncaged: Faces of Sigil" sourcebook, however, there's another reason why she insists on being called king over queen: "she" is actually a transsexual, who dresses up like, acts like and basically pretends to be female to the point it's whispered she's given birth to a tiefling daughter, as pretty much everybody is fooled.
In Final Fantasy VIII, the Card Club uses card terminology for all its members. The club's leader, Quistis, is the female "King". She actually won the title from the Garden's doctor, who is also female.
Fire Emblem Awakening: In the Japanese version, Emmeryn's formal title is "Holy King"; outside of its use, everyone just calls her the queen. The English version removes any gender confusion by calling the ruler of Ylisse the "Exalt", a pretty much gender neutral term.
Additionally, one of Chrom's signature class skills, Rightful King, is also obtainable by his daughter Lucina.
In Quest for Glory V, the Rites of Rulership are in place to crown a King of Silmaria. Series Action Girl Elsa von Spielburg is in the running for it. Fortunately, few people treat this like it's a bad thing. Though the events of the game result in the Player Character being the first choice to become King, the player can refuse the throne, which will lead to Elsa taking it up in his stead. Nothing is made of what the result is if the player also chose to marry Elsa.
In SaGa Frontier, the human girl Asellus is made the "Prince" of Facinaturu, the Land of the Mystics. This is probably because a) there, "princess" is a term for Lord Orlouge's mistresses; and b) because the Mystics don't seem to care much about gender (this part of the game contains a lot of gay subtext.)
Symbolic application in Misfile. The best of the local street-racers is crowned 'King of the Mountain', and right now, that happens to be Ash, who is (currently) female. When she first won the title, they tried to change it to 'Queen of the Mountain', but due to her recent Gender Bender, she protested. LOUDLY.
Inverted in Looking for Group, where Richard has claimed (among many others) the title of "Mistress of Magma".
In Magience, Fae titles needn't match the holder's gender. The current King is female, and her late husband was Queen.
A More Personal Union: The Polish Sejm, worried that the throne of Poland will devolve to the Hapsburgs, promises to legitimize any child Sigismund II will have with his mistress. The child is female, and becomes King Augusta of Poland. Augusta becomes a TomboyAction Girl who - when pressured to have an heir - worries that her child will be a female again. The Sejm once again vows to accept any child, male or female, as an heir. Augusta has a daughter, who she names Jadwiga.
Gender Flipped in the Adventure Time episode "Princess Cookie," which featured a male character who wanted to be a princess. A female character also takes up the role of king.
Played straight in "Earth and Water", in which Flame Princess usurps her father and is referred to by her guards as "the new Flame King".
Inverted in Beast Wars where Inferno called Megatron his Queen, because Inferno was based on a fire ant. Megatron found this rather annoying, but grudgingly accepted it, as Inferno was one of his most powerful and reliable followers.
Inferno gets it from a glitch in his programming. The ant's instinct is dominant, so he truly believes that he is an ant.
Gender Flipped in an episode of The Fairly OddParents when Timmy is crowned Queen of the Skate Park (he won the title from Vicki), though his friends keep correcting him with "King" when he says "Queen".
Jim Button: Well, Li Si was considered for the position of King of the Sky Kingdom but she turned it down. Anyway, her father is the Emperor of Mandalia and it's not clear if she'll become Emperor or Empress once she inherits the throne.
The Simpsons: When The Simpsons bought a pool, Lisa became popular. Envious, Martin hired people to install a better one. He gloated to himself and the people building the pool about how Lisa thought she's the summer queen and then he said he would be the queen. Seeing their reactions, he quickly corrected himself by saying "King".
Older Than Dirt: Ancient Egypt had several female rulers from multiple dynasties:
Hatshepsut crowned herself Pharaoh and maintained an elaborate legal fiction of maleness. Because the Pharaoh was, mythologically speaking, the son of Ra, he had to be a man, even if he was a woman. She even insisted on being called "His Majesty". Statues of her go so far as to depict her with a male body, but an obviously female face. The traditional false beard worn even by male pharaohs was especially necessary in her case.
Sobekneferu (reigned 1806–1802 BCE) is the first known female King of Egypt, which makes her the Ur Example of this trope. She reigned during the twelfth dynasty, but women might have been crowned King as far back as the first.
Likewise, Cleopatra, usually described as "Queen of Egypt" actually held the title of Pharaoh. She and her brother (who were married) constantly vied for the throne until his untimely death, and then another younger brother became her co-ruler before he died as well, leaving her sole ruler.
Jadwiga of Anjou, King of Poland. This one is a fine case of Loophole Abuse: Although the law made no provision for a ruling queen (Regina Poloniae), no law said that the king had to be male. By crowning a woman King, Poland avoided a Succession Crisis.
This happened again in 1575 when Anna Jagiellon was crowned as "King of Poland" and co-ruler with her spouse Stephen Bathory.
Although the Latin word for "Queen" is "Regina", Elizabeth I of England ruled as Elizabeth Rex; Rex is Latin for "King". In one famous speech, she stated that even though she had the body of a woman, she had the heart and stomach of a King of England. Then her navy went out to kick the Spanish Armada's ass.
Her mother Anne Boleyn was made the Marquess of Pembroke (a masculine title, despite the feminine-looking ending) prior to her marriage by her future husband Henry VIII. The actual female equivalent is "marchioness"note Pronounced 'martian-ess'. She was given the masculine title because she held the rank in her own right, rather than by marriage.
Elizabeth's elder half-sister, Mary I, was never created Princess of Wales, as that title is reserved solely for the wife of the monarch's heir presumptive. However, for many years she was their father's only legitimate heir, so she lived at Ludlow (the official residence of the Prince of Wales) and was permitted to use the livery colors and seal of the Prince of Wales. Many nobles and scholars of the day considered her to hold the rank in all but official capacity; her tutor, Juan Vives, dedicated one of his works to "the Lady Mary, Prince of Wales."
Queen Elizabeth II is the Lord of Mann (on the Isle of Man), since English titles held by the monarch revert to the crown, which is why Cornwall is recreated every reign.
She is likewise the Duke not Duchess of Normandy, in her capacity as the ruler of the Channel Islands, and the Duke of Lancaster in Lancashire.
During World War II, her father George VI was encouraged to invest Princess Elizabeth as Prince(ss) of Wales in her own right in order to help secure the loyalty of the restive Welsh. He refused, citing the status reference above (which is silly, because the Crown is the font of all honours and he could have done it anyway); in place of the title, Elizabeth was invested in the Gorsedd (the Welsh order of bards and a fairly big deal), and toured Wales more often.
Historically, the ruler of Hungary was required by law to be a King. So, the two female rulers of Hungary, Mary of the House of Anjou (a sister of the Polish King Jadwiga above, by the way) and Maria Theresa, were formally titled Kings of Hungary.
Averted with Maria Theresa's main title, Holy Roman Empress. While she ruled in her own right as Archduchess of Austria, Queen of Bohemia, etc., etc., etc., she was officially only Empress-consort (or later, Dowager Empress): the Electors refused to elect a female Emperor, giving the title to her husband Francis, Duke of Lorraine. In practice, Francis left governance to his wife, with most of his own efforts going to the Empire's finances.
Peggielene Bartels, the first female king of Otuam, Ghana ("king" here being more of a local village-leader position).
Irene of Athens was imperial regent of the Byzantine Empire during the reign of her son Constantine VI (780-797). Upon his death she took the throne, ruling as "emperor" rather than "empress".
Inverted with Elagabalus, a third century Roman emperor who much to the dismay of his subjects preferred to be referred to as "empress", and who would (probably) be considered transsexual by today's standards.
Tamar of Georgia was known as King of Kings and Queen of Queens, and she is always referred to in the Georgian language as King Tamar.
Christina of Sweden, nicknamed "the Girl King," was educated in typically masculine pursuits, and took her coronation oath as King, not Queen Regnant.
The legal title for the Dutch monarch is "King of the Netherlands", regardless of gender. So while every monarch from Wilhelmina through Beatrix has been commonly called the Queen, legally the Netherlands has always been ruled by a King. It just so happens that Willem-Alexander is the first male King in 122 years. As the Netherlands follows Absolute Primogeniture (the eldest child inherits, regardless of gender) and he has three daughters, the heiress apparent is Catharina-Amalia, Princessof Orange.
Similarly, the constitution of Denmark defines just the office of "The King", while also specifying explicitly that this office can be inherited by women. Any particular female king will be referred to as "queen" even in formal, official documents.
The Scottish cities of Aberdeen, Dundee, Edinburgh and Glasgow all have a Lord Provost instead of a mayor. Anyone who holds the title is referred to as Lord Provost, regardless of gender.
This is true of many other positions in the UK with "Lord" in them, including the offices of Lord Privy Seal, Lord President of the Council, and Lord Chancellor (three very senior positions in HM Government—about which see more below—typically held by very big fish indeed). Thus far, no woman has ever been Lord Chancellor, but the other two have been held by women: Harriet "Three Hats" Harman was Privy Seal 2007-2010, and five women were Lord President under Tony Blair and Gordon Brownnote In fact, men only held the office for three of the twelve years of Labour government, and the last one of those was Peter Mandelson, who took the office only to worm his way into the government of his hated rival, Brown., and all of them continued to use "Lord" rather than "Lady".
There is a reason (probably) that no women have been Lord Chancellor just yet. Lord Privy Seal and Lord President are emphatically political positions—they are generally being given as a sinecure to bring someone with a more pragmatic but less prestigious title like Deputy Prime Ministernote e.g. David Cameron making Nick Clegg Lord President or Leader of the House of Commonsnote as usually happens with Privy Seal into Cabinet. However, the Lord Chancellor was, until 2005, the the speaker of the House of Lords and a government minister responsible for the judiciary and sat on a number of judicial and quasi-judicial bodies, as well. As such, the Lord Chancellor was always both a barrister (almost always a Queen's Counsel) and a Peer—and even today, these are very much male-dominated areas (to give an idea, of 443 applications for silk in 2005-06, only 68 were submitted by women; of the 175 actually appointed QC, only 33 were women—better than the average, but there was a conscious effort to create more women silks). To streamline the government, Labour decided to strip the post of Lord Chancellor of almost all its powers and create the positions of Secretary of State for Justice and Lord Speaker with most of the post's old executive and legislative duties, respectively. Thus far, all three Justice Secretaries have been Lord Chancellor, and if a woman is appointed to the post, it is likely she will be called "Lord Chancellor"; somewhat amusingly, both Lord Speakers since the establishment of the post have been women, and both followed the same rule.
Many corporate boards still title their presiding member "Chairman" regardless of the incumbent's gender. Others truncate to "Chair" to avoid both gender bias and awkward back-creations like "Chairperson".
Examples of gender neutral titles
Black Lotus and Scarlet Rain from Accel World are the kings of their respected domains.
Similarly White Cosmos, the White King, head of the Acceleration Research Society and Black Lotus's elder sister. Purple Thorn both uses this trope as the Purple King and averts is with her nicknameEmpress Voltage
In Maoyuu Maou Yuusha, the main female character holds the title of "Maou" which can be translated as "Demon Lord" or "Demon King", but in it's original Japanese form, the title is unisex.
In The Twelve Kingdoms, the ruler is referred to as the "king" regardless of gender (at least in some translations). The original Japanese word translated as "king" is closer to the gender-neutral "monarch".
In the dub of Magical Girl Lyrical Nanoha A's and some translations, Signum, Zafira and Reinforce refer to Hayate as "Master Hayate" (or "Meister Hayate"). The original Japanese title they use for her is "Aruji", which is gender-neutral.
The title of "King of the Pirates" in One Piece has both male and female pirates striving for it, as well as some whose sex is unclear.
Likewise, the titles "Shichibukai" and "Yonkou" are translated as Seven Warlords of the Sea and the Four Emperors, even though at least one member of each has been female.
In ElfQuest, Winnowill becomes "Lord Winnowill" after Lord Voll's death.
In Fables, the North Wind is referred to as a king regardless of the gender of the current incarnation. When Mr North pulls a Heroic Sacrifice, he is succeeded by his granddaughter Winter, and her courtiers explain to her parents that the word "queen" means something different from what the North Wind should be.
Live Action Television
In the re-imagined Battlestar Galactica, officers and officials of both genders are referred to as "Sir."
In the Branion series by Fiona Patton, the sovereign's title ("Aristok") is unisex, and all the others are male (Prince, Duke, Knight, etc) but can equally well pertain to females. A consort, whether male or female, is just that, a consort.
In Patricia C. Wrede's Dragonsbane (also titled Dealing with Dragons), the first volume of the Enchanted Forest Chronicles, the title of King of the Dragons is gender neutral: Kazul is a female dragon and a perfectly legitimate contestant for the title of King. In what is arguably an inversion, Queen, a boring secretarial position unrelated to being the ruler or ruler's consort, is also a gender-neutral title, and the most recent holder of the now-vacant post was male.
In The Fifth Elephant, the supreme dwarf ruler is always and ever "the Low King", no matter what genitalia the current King has. Discworld dwarves have historically refused to recognize gender at all, although it has been hinted several times that the current Low King might be female and unashamed of the fact. Confirmed in Raising Steam.
In A Song of Ice and Fire, a certain key prophecy refers to The Prince That Was Promised, but most of the signs are pointing very clearly at a female character, Daenerys Targaryen. The fandom guessed that the term translated as "Prince" was gender-neutral in Old Valyrian, the original language of the prophecy. This was proven exactly correct in A Feast For Crows: all Valyrian nouns are gender-neutral. If Dany's late brother Rhaegar, who thought the prophecy referred either to him or to his son, had taken that into consideration, it might have spared the kingdoms some grief in the Backstory.
Played straight in the Destroyermen series. The term "high chief" is used for both males and females, contrary to using "chieftess" with even a character lampshading it. It is averted, however, in the kingdoms of Aryaal and B'mbaado, where the terms "king" and "queen" are used for the respective genders.
Gifts, the first book in Annals Of The Western Shore, uses "brantor" for the heads of the Upland families. While most of the brantors seen in the story are men, female brantors like Parn Barre aren't too uncommon. When someone from the more sexist lowlands insists on calling her a "lady-brantor", Orrec and Gry find it ridiculous.
The ruler of the city of Liavek is always called the Levar, regardless of sex.
In the Chronicles of the Kencyrath, the title of lordan (the heir to a lord) is gender neutral... somewhat to the surprise of most of the Kencyr Highborn, who had become accustomed to only appointing men to that rank. Two women hold the rank in the series: Kirien, whose own House Jaran's research found the title to be unisex; and Jame of Knorth, the series protagonist.
In Judaism, any number of verses, both in the Bible and in other sources, refer to God in the feminine form instead of the more common masculine form. This isn't to suggest that God is a female being, but rather one that can be referred to both in the masculine and feminine gender. An omnipotent being likely doesn't have fixed genitalia.
From the Fire Emblem series, Lyn and Eirika both start out with the Lord class, with Lyn promoting to Blade Lord and Eirika to Great Lord. This is mostly a case of Gameplay and Story Segregation, however, as Lord is the traditional class for any protagonist of royal ancestry, regardless of what their actual title may be. Both Lyn and Erika are princesses and referred to as such in their respective games.
The Daedric Princes of the Elder Scrolls series are an interesting example. They don't actually have set genders due to their nature, but since almost all of them tend to adopt distinctly male or female forms this trope is effectively in place.
Likewise, in The Elder Scrolls V: Skyrim the Jarls (pronounced "Yarls" and taken from an old Scandinavian term for "Earl") can be either male or female, and apparently children can inherit the title from their parents regardless of gender.
Most republican titles, such as president and prime minister, are gender neutral (at least in English), with an exception noted below (senator/senatrix).
However, the specific form of address is gender-specific. So, while it might be President Hillary Clinton, when speaking to her, it will definitely be "Madam President". Inverted, in that no one is really sure what we'd be calling Bill at that time, since while the first person method of address is clear ("Sir"), the title isn't. The First Man ?? The First Dude ??? It gets even worse when considering Bill Clinton is a former President himself, and thus, usually afforded the title "Former-President Clinton" and address of "Mr. President". See, this is what happens when you letwomen into the clubhouse
In the case of the Philippines, which has had two female presidents, they refer to her husband as "The First Gentleman", a sensible counterpart to "First Lady".
While under current law women are barred from the line of succession, eight women have ascended Japan's Chrysanthemum Throne during its history. All of them used the same title as their male counterparts: "tennō". While the title is normally translated as the masculine "Emperor", the literal translation is "Heavenly Sovereign", which is gender-neutral.
Wu Zetian was the only woman to ever be crowned huangdi of China. Despite being monopolised by men, huangdi is not an inherently male title in any linguistic sense. Huangdi is translated as "Emperor" when the ruler in question is male, and Wu Zetian's title is usually rendered "Empress" in English. This is confusing as "Empress" is also used to translate a completely different Chinese title which means "Primary Consort of a Ruler". note Wu Zetian was given somewhat of a Historical Villain Upgrade after her reign due to some unsavoury things she did or ordered, but many modern historians believe she wasn't much worse than most male huangdi in terms of ethically questionable decisions. Much of the later vilification was either hostility towards the scandalous (at least to traditional Confucian values) idea of a female ruler, or was the typical propaganda a successor dynasty would produce about how awful the line of rulers it had replaced had been.
Blended and Other Examples
Anime and Manga
Ooku: Because of a Gendercide plague, the Tokugawa-era shoguns and feudal lords of Japan are all female but use mascunline names and titles. Audiences with foreigners are elaborately stage-managed to give the appearance that the ruler is male. By the time the story begins, almost everyone has forgotten that men used to be fully half the population and most people no longer understand the reasons for these customs. In the flashback arc that describes how this came to pass, the first female shogun (Iemitsu the Younger) was disguised as a man to hide that her father had died, with the intention being to restore male succession as soon as she produced a surviving son. When the last major opponent to female-line succession died, Iemitsu appeared at the fealty ceremony in female dress, commanded all to look upon her as shogun, and proceeded to rule in her own right until her death.
Revolutionary Girl Utena: The titular Utena often refers to the fact that she wants to be a prince, though in context it refers more to an ideal than an actual royal title, and the entire point of the series is to heavily deconstruct the ideals of both prince and princess.
Inverted in one episode of Anime/Slayers: one of the queen's consorts (in a matriarch society) was able to hide the crown prince's gender, as well as the gender of multiple members of the royal guard. The queen does NOT take this well. Nor does Zellos, who was dating said prince by mistake.
Winnowill in ElfQuest is Lord of the Gliders. A suggested reason is that the Gliders only ever had one ruler before that, and for something like 10,000 years, so she just took over the title.
In Fables, the North Wind is referred to as a king regardless of the gender of the current incarnation. When Mr North pulls a Heroic Sacrifice, he is succeeded by his granddaughter Winter, and her courtiers explain to her parents that the word "queen" means something different from what the North Wind should be.
In Heir Apparent, Giannine plays a role-playing game which ends up threatening her life through a fault in the machine in which the goal is to be crowned the king. Even if the player is a woman. Yeah, the designers didn't think that one through.
Tanith Lee’s East of Midnight features the Moon King, the female ruler of a female-dominated society.
In the Dragonlance saga, Dragon Highlord Kitiara is referred to by the masculine title because Dragon Highlady would have just sounded silly. Word of God has it that if the subject had ever come up in the story, Kitiara would have laughed and said she certainly wasn't a lady.
Though Kitiara does have some explicitly feminine nicknames (she is known as both the Blue Lady and the Dark Lady), in person she is always addressed by her followers as "Lord Kitiara" or "My Lord".
By the same logic, both male and female members of the ruling council of Tir Tairngire, from the Shadowrun game setting, are formally titled "Prince", because "Princess" carries so many silly Disney-cutesie connotations.
Live Action Television
In Angel, Illyria, God-King of the Primordium, is referred to as "she" after her resurrection. This is presumably because the Old Ones lacked any real gender identity, whereas she's now inhabiting a female body, which affects her personality. In her original language what's been translated as God-King was probably a genderless title.
It's revealed very late in Brütal Legend that the title of "Emperor" amongst the Tainted Coil can be used for either gender. In fact, the previous Emperor was the protagonist's mother.
Toyosatomimi no Miko of Touhou is a genderbent version of Crown Prince Shoutoku, and retains his (masculine) title. However, it isn't clear whether or not she was openly female.
In Fallout: New Vegas, the Sink Central Intelligence (which is programmed to act as a valet) adresses the protagonist as "Sir", even when you play a female character. If you bring up the subject, it will apologize and explain that it never were programmed to adress anyone in any other way (there's only one other notable female at the Big Empty, and she prefers to be called "doctor", nevermind being a brain in a jar with only a tenuous hold on gender identity), and it's hardcoded so it can't be changed.
In the Japanese version of Kid Icarus: Uprising the Goddess of Nature, Viridi, is named Naturé, King of Nature, despite being a goddess that looks like a little girl.
Storm Hawks: Master Cyclonis is the Empress of Cyclonia. This seems to have also been the title used by her Grandmother.
A very rare inversion comes in Viva Pinata. When Franklin Fizzlybear befriends a swarm of bee pinatas, he is eventually dubbed "Queen" for a short time. This being a swarm of bees, they probably couldn't think of another title. Franklin does not object to being called a queen.
When using Latin titles, swapping the "-or" for "-rix" is a general rule when the holder of a position is a woman. (This is seen in dominator/dominatrix. You may also know it by the anglicized suffix "-ess", as in actor/actress) Hence, the feminine form of the Latin word "senator" is "senatrix". The rule was once used with Latin-derived words in English, but this is now essentially extinct, which means "senatrix" is virtually unknown in English and "senator" is now considered unisex.
In modern Romanian, all political and professional titles are correctly and formally masculine, even if held by a woman - one is expected to address a female as "Mrs. Doctor" or "Mrs. Senator". Colloquial speech has multiple feminine titles but they are unsuitable for formal occasions.
It is the same in modern Russian, except the professional titles are rarely used to address. Some Russian language scholars classify words like "doctor" or "professor" as belonging to a fourth, "common" gender. And if you stick a feminine ending on some of these words, such as "general", you will get a word for "general's wife".
The French model for educators and administrators is similar to the Russian and Romanian examples above: in formal metropolitan French all offices and professional titles were and may still be masculine, so the correct way to address a woman in office is "Madame le Professeur" or "Madame le Juge". Other Francophone countries are less strict about this.
In modern Swedish, most professions use masculine titles regardless of the person's gender, such as "professor" or "doctor". The archaic feminine forms "proffesorska" and "doktorska" are hardly ever used except in period pieces and do not actually mean "female doctor" or "female professor" but "a woman married to a doctor or professor". The feminine title "sjuksköterska" ("nurse") is used by all nurses regardless of sex. The masculine equivalent, "sjukskötare" was already in use as "orderly", indicating much less professional training.
In Danish the situation is much like in Swedish (the two languages are closely related). A tongue in cheek inversion of the trope is the use of the word "kassedame" (literally "box lady", but idiomatically "cashier"), the joke being that it is not as much a title as a job description ("kasse" can also mean checkout).
Elizabeth I of England (mentioned above) also referred to herself in her speeches and writings as a "prince", as did her sister Mary I and cousin Mary, Queen of Scots While it had masculine connotations even at that time, "prince" was an accepted term for a sovereign ruler regardless or sex or title (it comes from princeps, a word meaning "first"). When Machiavelli talks of "princes" in Il Principe, he's referring to anyone in a position of ultimate authority.
Janet Yellen, successor to Federal Reserve Chairman Ben Bernanke, chose to use "Chair" rather than "Chairwoman" or "Chairperson" as her formal title. When newspapers tried to make hay from this tidbit, people pointed out that the usage was perfectly valid and that the word "chair" (in the sense of a head of a meeting) was actually coined before "chairman/woman". Likewise, "Chair" is now the preferred term in academia for the elected head of a university department.
Technically speaking, "king" is gender neutral-it derives from a word meaning "leader of the people" but most kings were male, and "queen" is thus derived from a word meaning "wife."