Maiden Aunt

Mortimer: "Aunt Abby, how can I believe you? There are twelve men down in the cellar and you admit you poisoned them."

Aunt Abby: "Yes, I did. But you don't think I'd stoop to telling a fib!"

—Arsenic and Old Lace

She's your favourite elderly relative. Never married, never thought about marrying, never had a boyfriend or a lover - or at least if she did you don't know about it. She's grey-haired, old-fashioned, conservative, prim, proper, prudish, strait-laced, and disapproving of anything new-fangled. She wears basic black with lace at the collar and cuffs and when she goes out she puts on a hat that went out of style in roughly 1920. But she dotes on her nieces and nephews, fusses over the local parson and the friendly neighbourhood policeman, and is sure to offer everyone 'a wee drop' of her special homemade cordial - which, it turns out, could put a 600-pound gorilla into a coma (and sometimes more) after one sip. She drinks it by the gallon with no ill effects.

Although unmarried elderly women have always existed, the Maiden Aunt as a trope first arose in the 1880s. Historically, women had shorter lifespans than men because of the dangers of childbirth: many men married more than once, meaning that any woman who didn't marry at a young age had a good chance of marrying later on. But in the mid-Victorian era women's life expectancies increased due to advances in modern medicine while men's lifespans decreased, partly due to civilian conscription during wartime and, as we know now, partly due to increasing use of tobacco. Suddenly there were myriads, even millions of women who had no chance of marrying and, unlike unmarried men, had little chance of immigrating to a place where they could find a spouse. Decades later, these women reached old age and became known as maiden aunts.

They were especially thick on the ground in the US in the 1900-1930 period and in the Commonwealth in the 1950-1980 period - these were the women whose potential husbands died in the US Civil War and in World War I, respectively. In the 1920s they were often known as "Victorian aunts", because they had grown up in (and for the most part never quite left) the Victorian era. Often also called "spinsters" and "old maids", although the latter term is usually discredited as offensive nowadays. If you were born in The Sixties you may remember how incredibly common they were, both in fiction and in Real Life.

Of course, many real-life women remained unmarried for reasons other than the one stated above. Some were lesbians, some were asexual, some preferred a career to marriage, some gave up the chance of marriage to look after aging parents, and some simply didn't want the bother of a husband and family. In fiction, though, they tend to be prudish, sexless conservatives who have never worked for a living. Some are kindly and sweet, some are bitter and angry, some are in a Cloudcuckooland. Often played straight in mysteries and for laughs in comedies. There aren't many subversions out there - younger audiences are usually squicked by any hint of sexuality in an older woman. A few characters fit this trope even though they aren't strictly speaking maidens.

A type of Old Maid. May be a Moral Guardian or a Nosy Neighbor (or both). Compare Little Old Lady Investigates, and Christmas Cake.

Not quite a Dead Horse Trope, but much less common these days than twenty or thirty years ago for various reasons. Can have Unfortunate Implications if a writer decides that "not having married a man" equates "not having done something with her life"; this implication is usually brought over as the main worry of an Old Maid.

Examples of Maiden Aunt include:

Comic Books

Although Spider-Man's Aunt May was married, she fits the trope as a widowed Maiden Aunt.
- She's getting married again, and she had some boyfriends, including Doc Ock. A lot of fans think of her as one, though.
  - Arguably, she's more of a Maiden Aunt in the newspaper comics than in the comic books.
- She was with Edwin Jarvis for a while, but then it turns out that that Jarvis ain't Jarvis. You're a Parker, May - your love life's gonna be chaos, it's the law!
- Anna Watson, MJ's aunt and May's best friend, is this to a certain extent as well (or at least the favorite relative and unmarried part).

Film

American actress Zasu Pitts was typecast in later life as a Maiden Aunt, appearing in dozens of movies and television shows.
Subverted in Aren't Men Beasts? (1937), in which the father of a slandered groom dresses up as a Maiden Aunt in order to clear his son of any wrongdoing.
Aunt Minerva in The Gift of Love: A Christmas Story.
When George Bailey gets the chance to find out how the world would have turned out if he'd never been born, he finds that his wife Mary had become a bitter, unhappy Maiden Aunt.
Most 40s and 50s series comedies featured Maiden Aunts, including the Mexican Spitfire series (Aunt Delia).
Tim Burton's Alice in Wonderland had Aunt Imogen. She wasn't so much "single" as "engaged to a prince who doesn't exist".
The main character's aunt in Hausu.
In The Heiress, Catherine ends up as a Maiden Aunt, doting on the children of her cousin Marian, who call her "Aunt Catherine".
Aunt Fanny in The Magnificent Ambersons.

Literature

Agatha Christie's Miss Marple plays this trope straight. When first introduced, she is a Victorian Aunt; in one of her last appearances in 1965, she alludes to having a Victorian Aunt.
- Of course, there's no contradiction there. Victoria reigned for 64 years until 1901, so if Miss Marple was born towards the end of the 19th century, as seems likely, her aunt(s) were almost certainly Victorian as well.
In Andre Norton's The Crystal Gryphon, Joisan's aunt, Dame Math, entered a religious order after an Arranged Marriage fell through upon the death of the groom. She left her order (but was still called 'Dame') after her brother was widowed, and ran his household for the rest of her life.
The titular character of Patricia Wentworth's Maud Silver mysteries: a governess who became a private investigator. She plays this trope straight - most of the stories show her writing letters to her nieces in her spare time, and she is at least an Edwardian (if not Victorian) throwback in terms of hairstyle, taste in interior decoration, and her love for Tennyson's poetry.
Patricia C. Wrede's and Caroline Stevermer's Sorcery and Cecelia has Aunt Elizabeth (who is chaperoning Cecy back home in the country) and Aunt Charlotte (chaperoning Kate and Georgina in London). At one point one of the girls speculates that Aunt Elizabeth is still unmarried because of a Grave Disappointment in her Youth (which turns out to be true, in a manner of speaking). Subverted in that Elizabeth gets married to Mr. Wrexton in the end.
Granny Weatherwax of Discworld probably counts. She's by far the most suspicious and conservative of the witches seen (although also the most magically powerful) and her title of "Granny" is definitely only honorary.
- Also subverted with Nanny Ogg, who's explicitly described as looking like this but had an... interesting life and is still entangled in an on-again, off-again relationship with the great dwarf lover Casanunda.
  - Looking? Nanny looks like the proverbial Dirty Old Woman, and acts the part.
L. M. Montgomery had a lot of these in her stories - but considering when they were written, that's not surprising.
Charley's Aunt gets a lot of mileage from this trope. Dona Lucia (although a widow, rather than never having married) is presumed by all five of the youngster to be one, although that's because they've never met her. (She isn't, by a long shot.) Babs plays her as one while masquerading as her. Mr Spettigue expected her to be one, so he never even considers that there might be an imposture going on. The real Dona Lucia takes full advantage of it.
The Widow Douglas from Mark Twain's works set in St. Petersburg, MO should count: Elderly, Wealthy, Conservative, no family mentioned, cares for the main cast...
Mrs. Figg is the Cloudcuckoolander variant, although it turns out that's partly Obfuscating Stupidity.
- Professor McGonagall, who superficially follows the strict-but-fair schoolmarm stereotype to a tee. However, as the series goes along, she reveals some Hidden Depths in the form of Not So Stoic, Never Mess with Granny, and Deadpan Snarker leanings. In the fandom, McGonagall is widely seen as a Cool Old Lady. (Word of God notes that she, like Dona Lucia above, is actually a widow rather than a spinster.)
- Also superficially following the schoolmarm stereotype is McGonagall's Evil Counterpart, Dolores Umbridge. When she's introduced, she's actually described as looking like "somebody's maiden aunt" and she affects the mannerisms of one, including an apparent love of cats. But it's only a thin veneer hiding a power-hungry, sadistic Complete Monster.
Aunt Peace and Aunt Plenty in Louisa May Alcott's Eight Cousins and Rose in Bloom.
The title character in Patrick Dennis' Auntie Mame is a notable subversion of the trope.
Matilda in The Full Matilda, but without the caring part. If anything she's more of a Deadpan Snarker. The book deconstructs her reasons for being one.
The Hardy Boys have Aunt Gertrude, a classic example of the trope. She often scolds the Hardys for their dangerous exploits while secretly cheering them on, and occasionally offers up some wisdom that gives them a hint of what direction to go next.

Live Action TV

Miss Emily and Miss Mamie Baldwin on The Waltons.
Aunt Bee on The Andy Griffith Show.
Aunt Ellen on Brendon Chase.
Aunt Harriet on the 1960s Batman live-action program.
Nugie on The Gale Storm Show.
Doña Clotilde in El Chavo del Ocho is a surprisingly more sexual (or at least romantic) take on this, but her attempts of "seduction" (almost always involving hugging or bringing food) always fail with her intended target, and she is quite the traditionalist anyway.
Invoked Trope in an episode of 30 Rock. After one too many romantic failures, Liz gave up on dating and decided to start her "graceful transition into spinsterhood". This included buying a cat and naming it "Emily Dickinson" as well as joining a book club reading Murder on the Orient Express. Of course, she reverted to her normal self by the end of the episode.
Hilda and Zelda of Sabrina the Teenage Witch come off this way, despite not being as old as this trope usually implies (or at least, not looking as old). Zelda was briefly married back in the Middle Ages while Hilda leaves the show after getting hitched in the later seasons.

Theater

Aunt Abby and Aunt Martha Brewster in the play and movie Arsenic and Old Lace. Their special cordial is extremely special.
Juliana Tesman in Hedda Gabler.
The Nutcracker features two Maiden Aunt characters.

Video Games

Mrs. Crumplebottom from The Sims
Sialeeds in Suikoden V is this to the Prince. Very understandable considering what she, Arshtat, and Haswar had gone through. Come to think of it, Haswar does count for this trope as well.
Wendy Oldbag (or Windy Old Bag?) from the Phoenix Wright series. She's often seen hitting on Miles Edgeworth, who's probably young enough to be her son.

Western Animation

Granny in the Sylvester And Tweety cartoons is probably a maiden aunt, as her family is never seen.
Patty and Selma Bouvier in The Simpsons were this at first, though Selma ultimately had multiple marriages, none of which lasted very long. Patty apparently lived a life of self-imposed celibacy (despite dating Skinner for a while), but more recently came out of the closet as a lesbian and nearly married before finding out her would-be bride was a man in drag.
- Great Aunt Gladys, Marge's aunt, seems to fill this trope. In her video will, she warns Patty and Selma about "not Dying Alone."