A Little Princess. To clarify, Sara Crewe considers herself to be a princess and looks to various royal women in history as role models. Though her attitude isn't because of her money (she's actually Spoiled Sweet), she considers herself to be a princess because she acts grand and dignified, and would never do something vulgar. In one film adaptation, she makes a big speech about how all girls are princesses.
Averted in Ella Enchanted. She marries a Prince, yet specifically requests not to be a Princess.
Lloyd Alexander's Chronicles of Prydain: The chatty redhead who gets protagonist Taran out of a scrape (and proceeds to irritate him for the rest of the book) in The Book of Three turns out to be "Eilonwy daughter of Angharad daughter of Regat of the Royal House of Llyr." She's the last surviving member of a royal, magic-wielding bloodline. The complications of her ancestry form the plot of the third book in the series. Justified, somewhat, in that Prydain is based on ancient Wales, which did have a number of sub-kingdoms united under the rule of a single High King. So finding a stray princess wandering around Prydain was less contrived than it might be in another fictional country. Taran was pretty startled by the revelation, though. He was still getting used to the idea of royalty not always looking (or acting) how he imagined. (There's also the fact that they'd spent most of the book together, and he didn't find out she was a princess until literally the last page because Eilonwy never thought it was important enough to mention.)
In the John Carter of Mars series, Mars has many, beginning with Dejah Thoris, the title character of A Princess of Mars. Thuvia, Maid of Mars. Tara in Chessmen of Mars. Valla Dia in The Master Mind of Mars. And many others. Not always evident at first.
The Amtor series has Duare of Vepaja, the Venusian princess and Carson Napier's love interest.
Nah-ee-lah, the title character of The Moon Maid, is Princess of Laythe.
The Princess Diaries seems to embrace this, so say the pretty covers and The Film of the Book. Actually, the books go into a lot of politics and how "I Just Want to Be Normal" is not such an odd complaint if you happen to become a princess. The protagonist's grandmother especially is used to dash the princess dream; besides the ridiculous self-preserving measures she uses on the titular princess, dear old Grandmere also refuses to let her ex-daughter-in-law invite her own friends to her own wedding, feeling embarrassed by them, and instead invites the likes of Martha Stewart and Coco Chanel. Mia's Soapbox Sadie friend is used in contrast to say that the monarchy is outdated and its glamour far too overrated.
In the eleventh book of A Series of Unfortunate Events, spoilt brat Carmelita Spats dresses up as a "tap-dancing ballerina fairy princess veterinarian."
You want a princess? There's, like, hundreds of princesses in War and Peace. There aren't even that many princes. Justified because in Imperial Russia, the title could (and usually did) mean the top rank of non-royal nobility. There were princ(ess)es of Imperial blood, who were actually related to the Tsar, and there were the noble-but-not-royal kind. Royal princesses were usually titled Grand Duchess rather than Princess, the implication of the title being that they ranked higher than a regular princess. Since other princesses were non-royal, this was accurate. Grand Duchesses were the direct relatives of the Emperor. Indirect ones were titled prince(ss)es of imperial blood.note The confusion is due to different conventions of translating the Russian terms into other languages. In imperial Russia there were the dignities of knyaz and knyaginya, which is usually translated as "prince" and "princess", so the higher rank of respectively veliki knyaz and velikaya knyaginya correctly should be translated as "grand prince" and "grand princess", not "grand duke" and "grand duchess". In German for instance, which also differentiates between princes and princesses who are merely non-reigning members of a reigning family (Prinz and Prinzessin) and those who actually rule a principality (e. g. the Fürst and Fürstin of Liechtenstein), the higher Russian ranks are translated as Großfürst and Großfürstin).
Interestingly enough, while The Lord of the Rings features royally-connected ladies like Galadriel, Arwen, and Éowyn, the title "princess" is never actually used, though "prince" is.
Land of Oz series: Oz's Princess Ozma and Princess Dorothy. Ozma is a ruling princess, although Oz is explicitly described as being a kingdom; she makes Dorothy a princess in her own right because of how much the people love her and how much she's helped the realm.
Averted in The Wheel of Time. Elayne is the daughter of a queen and presumptive heir to the throne of Andor, but though the word "princess" appears exactly once, referenced as an archaic title that had long ago fallen out of use, "Daughter-heir" is used with the same frequency and arrogance.
In the third Book of Swords, Mark rescues a young woman from a cage in Vilkata's camp. No, he was not sent to rescue her nor did he have any idea who she was. Both are seriously wounded, but thanks to The Power of Love (quite literally by summoning Aphrodite) they both survive. And inexplicably, the woman turns out to be the Princess, though she is the top Royal and is obviously in charge, of the lands Mark was sent to. Though neither of them knew it until her people cheer her.
Averted in The War Gods series. Although the main character is technically a prince, he's way way down the list to inherit the throne and Word of God states he won't be king. Further he's the son of a king, but the king was chosen from all the tribal chiefs of their people. It gets further complicated with many different cultures and a rash of history that leaves the king of as least one good size country using the title of baron due to the historical king being long dead and no noble above king surviving the Godamerung. So far most of the women saved in the series tend to be lower class being abused by evil royals. And the badass female warriors all have lower class backgrounds.
Averted in The Council Wars by none of the good guys having true royals. The government is a republic modeled off Rome.
While the princess stared bewildered, with her head just inside the door, the old lady lifted hers, and said, in a sweet, but old and rather shaky voice, which mingled very pleasantly with the continued hum of her wheel: "Come in, my dear; come in. I am glad to see you." That the princess was a real princess you might see now quite plainly; for she didn't hang on to the handle of the door, and stare without moving, as I have known some do who ought to have been princesses but were only rather vulgar little girls. She did as she was told, stepped inside the door at once, and shut it gently behind her.
Quite literal in The Phantom Tollbooth, with the Princesses of Sweet Rhyme and Pure Reason, of the Kingdom of Wisdom. They are apparently high enough in authority that their brothers King Azaz and the Mathemagician, rulers of their own respective countries, appeal to them when there's a dispute... and once they're banished, Wisdom goes to Hell in a handbasket. It's only after they're rescued in The Quest that the Kingdom becomes sane again... everything is, in fact, better with them in charge.
Averted when the two Pevensie girls, Susan and Lucy, become Queens of Narnia in the first book, bypassing Princess altogether.
We get two quasi-princesses in The Horse and His Boy. Aravis and Lasaraleen are daughters of high ranking officials in Calormen, so they're not technically princesses (their title is "Tarkheena" - female equivalent to "Tarkhan") though Lasaraleen indeed acts like a stereotypical princess. Aravis eventually marries the heir to the throne of Archenland, making her a princess in the classic sense and presumably eventually a Queen.
Chronicles of the Kencyrath: Averted with Jame, who is effectively a princess but is never mentioned with that title. Jame's father, and later her brother, are both effectively kings but in their culture their rules hold the title of "Highlord." By birth, Jame simply has the title "Lady," the same as all Highborn women. She also holds the title "Lordan" (the gender-neutral title held by a lord's—including a highlord's—heir) because her brother chooses to bestow it on her. In their culture, people can pick any relative to be their heir, and female lordan are almost unheard of.
In Four Kids, Three Cats, Two Cows, One Witch (maybe) when the children are telling their individual stories, both Gerard and Beverley add princesses into theirs. Gerard admits his would work without a princess and says she could just be an heiress or some woman of property. Beverley's story serves to subvert Standard Hero Reward so including a princess was definitely intentional with her.
Definitely The Faerie Path series by Frewin Jones, where seven main characters are princesses.
Another aversion comes from Mary de Morgan's ''The Necklace of Princess Fioremonde" about an evil princess who traps her suitors' spirits in the beads of her necklace.
The protagonist herself, after she was awarded with a right to found her own steading (a sort of a semi-independent nation in the allied Protectorate of Grayson), has been more of an actual royalty, but before she had any issue, it was her (60 years younger) kid sister who was the heir to her steading.
Admiral Michelle "Mike" Henke, (later) Countess Gold Peak, the protagonist's best friend, is actually a first cousin of Her Majesty the Queen herself through their common grandmother.
The first member of the Manticorian Royal Family adopted by a treecat was Princess Adrienne, later Queen Adrienne I of Manticore.
Princess Ruth (the stepdaughter of Queen Elizabeth III's brother Prince Michael) was the first member of the Royal Family to become a spy.
Lieutenant Abigail Hearns of the Grayson Space Navy is, in all practical terms, a princess, although her actual title as the daughter of a Steadholder is the far less assuming Miss Owens (Honor's sister Faith was, correspondingly, called Miss Harrington).
The book The Shadow of Saganami centers on a ship whose officers included Miss Owens and Midshipman Helen Zilwicki, the stepsister of Queen Berry of Torch (Helen's dad adopted Berry before she was royalty). Their captain observes with a bit of humor that they appear to have a surplus of princesses embarked on this mission.
Before that, Berry Zilwicki had her own share of the adventures in the Crown of Slaves with her friend, the aforementioned Princess Ruth Winton, though she wasn't a Queen yet, and it was the very same adventures, in fact, that had led to the Kingdom of Torch's establishment.
Averted in the Safehold series by David Weber. The lead female character is beautiful, headstrong, and most importantly, spunky, but she's an actual queen.
There has been a recent trend in religious books geared towards young girls (toddlers to teens) to remind them that they're "God's Special Princess!" Boys are not told they are princes. They are "God's Mighty Warrior!" Make of that what you will.
Cheerfully played with in the novel The Ordinary Princess. The title character is the youngest child of a king and queen whose daughters are all named for jewels; she is Amethyst. When her fairy godmother gives her the gift of being ordinary, she becomes perfectly plain-looking and prefers to go by the name of Amy.
In Cry of the Icemark, Thirrin starts as a princess, interestingly, we first encounter her out hunting. She does go on to be a warrior queen so your mileage may vary.
The warlord Manzai from Chorus Skating evidently believed this in-universe, as he collected princesses abducted from neighboring countries. The party that freed his collectibles found this trope subverted when their five rescued charges prove to be quite a handful.
Presumably in a parody of the many stories featuring a princess as a Damsel in Distress kidnapped by some sort of monster, the Mediochre Q Seth Series mentions that dragons like to collect beautiful virgin princesses, along with gold and shiny things. Of course, nowadays most monarchies have long-since disbanded, but it appears that no-one has told the dragons this: the dragon Deep Ocean in the first book has a kidnapped French girl with no idea that she's technically the first in line to some non-existent throne somewhere.
In Seanan McGuire's Velveteen vs. series, the Princess derives her superpowers from the collective notion of "princess" as held by the little girls of the world.
Tara Duncanexaggerates this trope with all female prominent characters being princesses more or less officially; Tara is an heiress of the imperial category(along with her long-lost sister)while her friends Sparrow and Fafnir are respectively non-heiress princess and The Chief's Daughter. The female dragon Charm is later revealed being a princess too, like the demon Sanhexia.
The Apprentice Rogue: Deconstructed. This story shows what a real life princess could expect; cloistered to preserve her chastity and then married off for political alliance without her input.
The Last Dragon Chronicles: The female Pennykettles are all examples, being descended from royalty. More specifically, dragon royalty. Technicalities. What can ya do?
In The Underland Chronicles, the crawlers refer to Boots as "the princess", and she spends almost all of Gregor and the Marks of Secret in a princess costume.
Largely averted in the Heralds of Valdemar novels. There is only one central character who is a princesss, Elspeth the heir of Valdemar, and in her case the focus is entirely on the duties and responsibilities that weigh on a girl who needs to be prepared to take the throne someday.
In The Empress Game, the Sakien Empire has no shortage of them, and the titular Empress Game is a gladiatorial combat between them. The protagonist impersonates one (and secretly, is one from a different place). That said, "princess" is defined fairly broadly — daughters of non-monarchical authority figures (religious leaders, for example) seem to qualify as well as royalty.