You Can Leave Your Hat On

A striptease. Depending on the tastefulness of the scene and the point in their career, it can either make or destroy an actor or actress.

Because someone disrobing on camera has a tendency to do that. Can go all the way; use of Scenery Censor and other camera hiding techniques is optional; may be played for comedy or pure weapons-grade Fan Service.

In the days of VHS rentals, this could cause technical difficulties, as that small section of the tape would get an inordinate amount of wear.

The trope name comes from the 1972 song "(You Can) Leave Your Hat On" by Randy Newman. Sung by Joe Cocker in the movie 9½ Weeks, as well as covered by other singers. Made popular again by Tom Jones's version in The Full Monty. Made ridiculous by Troll 2.

If an unwilling subject is forced to disrobe, it falls rather into Shameful Strip.

Has nothing to do with Please Keep Your Hat On, despite being extremely similar in name.

No real life examples, please; we'd be here all day.

Examples of You Can Leave Your Hat On include:

Females

Anime & Manga

Mahou Sensei Negima has an interesting variation on this. The girls go with Negi to Konoka's temple complex, and they create a bunch of magical decoys to take the girls' place so no-one will notice their absence. The clones then decide to do a striptease act for some reason. Surprisingly, it hasn't caused too much trouble (at least not compared to the release of the really big demon in the meantime).
Dominion Tank Police: In the first OVA, the Puma sisters perform a mirror striptease out of their Naughty Nurse Outfits to distract the police troops coming to apprehend them. It works.
Panty and Stocking With Garterbelt uses a striptease, complete with pole-dancing, as the Transformation Sequence when it goes normally.

Comic Books

Barbarella
Sin City has a character who is actually a stripper. In fact, she is sometimes depicted wearing nothing but a hat, invoking this trope to the T.
Jack Faust has Promethea strip for him at the start of their sexual encounter/magic lesson.
Omaha the Cat Dancer. The story is about a stripper and, well, actually involves striptease.
Not surprisingly, it happens in Little Ego, during one of the heroin's many Erotic Dreams. While stranded in the desert, Ego's guide recommends she remove her clothing. As Ego is disrobing, the scenery changes around her and she finds herself performing a striptease on stage.

Films -- Live-Action

Metropolis (1927). Robot Maria.
The Spy Who Came in from the Cold. Nipple-and-Dimed, but leaving you wondering how the BBFC gave it a PG rating.
9½ Weeks
True Lies
Dogma features Salma Hayek bouncing around to "Candy Girl". The scene is mesmerizing.
Rita Hayworth removes her gloves in Gilda (they're one of those long ones), 1946 being the era of the Hays Code. Her character ends up becoming one of the best known Femme Fatale characters in history. In-story, she would've gone further, but was stopped by her jealous husband.
Troll 2, which even used the trope naming song. And some corn.
Watchmen, and in some circles the scene has been not-so-affectionately dubbed "the porn scene".
Sophia Loren has a great one in Vittorio De Sica's Ieri, oggi, domani (Yesterday, Today, and Tomorrow).
Striptease. It's not actualy about a stripclub, but just about 1/4 of the movie is spend watching one of the girls in the club—usualy the main character—strip.
The opening scene of Barb Wire.
Les Chevaliers du ciel features a strip-tease atop a gorgeous Vought F4U corsair.
In Working Girl, Tess comes upon Mick knocking boots with Doreen Dimucci, both naked and yet figleafed. It's less than two seconds though.
Showgirls, of course.
Jane Fonda stripping off constitutes the entire opening credits sequence of the movie version of the aforementioned Barbarella.
Woody Allen's What's Up, Tiger Lily? has a woman doing a striptease over the end credits, as Allen lounges on a couch eating an apple—at the end he turns to us and says "I told her I'd get her in the picture... somewhere." The movie itself begins in a strip club, where one man remarks of the stripper "I liked her better in The Sound of Music."
In Coyote Ugly, Violet slowly strips for her boyfriend as part of an explanation of how she feels when she tries to perform on-stage.
Takin' It Off and Takin' It All Off with Kitten Natividad are all about this trope.
Party Plane is about stewardesses doubling as in-flight strippers.
Any movie by Ed Hansen is this trope, really.
Xuxa's character does a strip dressed as a teddy bear in Amor Estranho Amor.
In Hasta El Viento Tiene Miedo, Norma Lazareno's character (Kitty) does a strip for the other girls before seeing the ghost. The 2007 remake goes a bit further to topless nudity.
In Private Lessons, Sylvia Kristel's character strips for Philip, the young main protagonist.
In Sabato Italiano, Francesca Neri's character (Marina) is hired by a group of boys to perform a strip for them.
In Flodders 2, Kees (Tatjana Simic) performs a strip wearing a traditional dutch outfit.
Plucking the Daisy, one of Brigitte Bardot's first movies, has her performing in an amateur strip contest to earn money to pay for a rare book she mistakenly sold. It's mostly tease but the strip performed by the contestant just before her (in the uncensored version) goes all the way to full nudity.
Another of Brigitte Bardot's movies, Viva Maria, has her and her companion inadvertently inventing striptease while performing in Mexico.
In Canadian movie Le Party, Alexandra (Charlotte Laurier) performs a full strip for the prisoners in jail.
In Doctor in Trouble, Dawn (Janet Mahoney) performs a strip for the passengers on a cruise ship.
In Varsity Blues, the boys go to a strip club and are suprised to find out the performing stripper in none other than their Sex-Ed teacher, Miss Davis (Tonie Perensky).
In How to Beat the High Co$t of Living, Elaine (Jane Curtin) performs an impromptu striptease to distract the crowd and security from the ongoing heist.
In Delusions of Grandeur, Alice Sapritch's character performs a strip after one of the main protagonists mistakenly declares his love for her.
The Nude Set has an interrupted strip by the main protagonist, Sophie (Agnes Laurent), a strip by a cancan dancer earlier in the movie, a strip dice act, and a few more.
In Nashville, Gwen Welles does a strip after failing to impress the audience with her singing.
In One Night Only, Chantale Perron's character performs a strip at the party.
In Vive les femmes!, Viviane (Catherine Leprince) does a strip on top of the table at the New Year's dinner party.
In Prunelle Blues, the eponymous Prunelle (Valerie Steffen) does a strip on stage at the very beginning of the movie.
Escape to Athena (1979). The POW's put on a variety act for their German guards, the climax of which is a strip show by an interned female USO performer. While the Germans are busy leering over her performance, the Greek Resistance sneak up and take them all prisoner.
Sunset Strip (1993), as the name suggests, has many strip acts throughout.
In The Playbirds (1978), Penny Spencer and Mary Millington's characters must perform a strip to qualify for an undercover job.

Literature

In Carl Hiaasen's most famous novel, Strip Tease, Erin is a stripper and he describes her stripping fairly graphically at times. Much like bowling in The Big Lebowski, however, stripping is incidental to the plot of the book, only used as a setting and occasionally a source of the action.
1001 Tales of Arabian Nights has one particularly rowdy tale where three gorgeous sisters pick up a porter, get ridiculously drunk and then each strip in succession for the porter, who then returns the favor. Can't remember any of the other 1000 nights....
Spellsinger features a stoat performing an elaborate exotic dance in a bar. The human hero Jon-Tom is horrified to find himself attracted to her, as he's not used to anthropomorphs.
Otherland features a Brain Bleach Fetish Retardant subversion in a virtual strip club catering to, shall we say, a more perverted clientele. The girl disrobing for the slavering customers isn't taking off her clothes, but her skin.

Live-Action TV

Baywatch has a scene with Carmen Electra. Guess what song she used for the striptease?
House. To wit: in order to remember a diagnosis after a commotion-induced amnesia, House goes on a Journey to the Center of the Mind, where he meets a mental image of Cuddy. Given that this is Dr. House, she is quickly given a costume switch into a Sexy Schoolwoman outfit and strips while helping with said diagnosis. It's more of a subversion, though, since she stops after he starts to lose focus. She then lampshades the whole thing by saying that he'd rather be diagnosing than indulging in fantasy. He then takes a third option.
Mad Men—twice (Nipple-and-Dimed, both times).
In Battlestar Galactica Reimagined, Head!Six disrobes while walking up the stairs to Baltar's head!bedroom.
Helga in Allo Allo has used this tactic several times to distract people. Amusingly, she only goes down to her attractive but complicated undergarments and bustier.
In Britain's Got Talent, a 35-year-old lady stripped down to nipple tassels and a basque. One fell off, resulting in ITV pixellating the breasts with two Union Jacks. She did not get klaxoned by anyone and got three yes votes. She also got 39 complaints sent to Ofcom for inappropiateness (it was aired just after the Watershed, but the show had started at 7.45pm). No ruling has been made as yet.
Lois Lane, on Smallville, undercover while Going for the Big Scoop. Although that was not "stripping", but a Bikini Bar. (She could have at least taken her hat off...)
In two different episodes of Cleopatra 2525, with the emphasis on "tease" in both cases.
In the Friends episode "The One with the Stripper", Monica hires a stripper for Chandler (because he didn't have a bachelor party), but she turns out to be a prostitute. Eventually, Monica herself does a striptease for him (but we don't see much of that).
Holly J, to show her appreciation for current friend with benefits Sav, gives him a little show. However, Degrassi is still a teen drama on during primetime she didn't go too far. She still ended up in a wonderfully fitting red cocktail dress with her hair down.
On Greys Anatomy, Cristina "comforts" an injured Burke with a striptease... only for his parents to walk in. Later, Mrs. Burke overhears Cristina referring to Bailey as "The Nazi" and gives her a dressing-down for it, causing Cristina to conclude "She thinks I'm a stripper. And a racist! She thinks I'm a racist stripper!"
Happens occasionally on MST3K movies, but notably, almost any time a woman removes clothes for any reason, Mike/Joel and the Bots treat it like a strip tease.

Servo: (as saxophone plays) Taaaaaaking off clothes music!

In season one of The Wire, the Barksdale organization's main base of operations was a strip club called Orlando's, so there were a great many scenes with background shots of strippers and dancers (many of whom were actual employees of the strip club they used for the location, according to creator David Simon). Supporting character Shardene Innes was a stripper who worked at the club, who we see performing once, disrobing to the waist.
The late 80s/early 90s italian game show Colpo Grosso (and its german version, Tutti Frutti) is all about this trope, with professional strippers and contestants performing stripteases in the course of the game.
In an episode of the first season of French-Canadian sitcom Du Tac au Tac, set in a talent agency (circa 1976), a stripper they want to hire performs her routine but is interrupted and hides when some mobsters come looking for her. Genevieve (France Castel), an employee who was against the whole thing, is then forced to do a strip to try to convince the mobsters she was the one the striptease music was playing for.
The spanish TV show Cronicas Marcianas used to have Susana Reche performing a striptease at the end of the show.
Another spanish TV show, Condicion Feminina, had strip shows by Daniela Blume.
There is also the game show Strip-Poker as the name implies.
The French show Wiz qui peut had striptease acts the live audience would vote on.
Also from France, the Narcisso Show had a female participant who would sing and strip.
In one episode of German comedy Zwei Himlische Töchter, Kikki (Ingrid Steeger) does a strip to coax a bull into boarding an airplane.

Music

The whole subject of Tom Waits' "Pasties and a G-String".
And do we need to mention (again) the trope name? Didn't think so...

Music Videos

Liv Tyler has a striptease scene in the Aerosmith video for "Crazy". Somewhat squicky in that it's the lead singer's daughter and all.
Kylie Minogue's video to "Put Yourself in My Place". She starts off floating around wearing a spacesuit...

Myths & Religions

This one even appears in the Fanon of The Bible.
- The relevant part of the Gospels merely state that Herodias' daughter "danced" and got the head of John the Baptist. The fanon (specifically Oscar Wilde's Salome) has it as something called "The Dance of the Seven Veils", where she wears precisely seven veils over her body and removes all seven of them.
- A non-fiction book about the Second World War mentions in passing that dramatisations of Bible stories were popular at the time, some, this one for example, moreso than others.
- Simlarly in the book of Esther the Persian king summonned his queen Vashti "wearing her royal crown, in order to display her beauty to the people and nobles, for she was lovely to look at" (which she refused to do, and he banished her for it). This has been interpreted by some to mean "wearing only her crown".

Pro Wrestling

In 1997, during an Extreme Championship Wrestling Pay-Per-View, damage to the ring caused a lengthy delay in the action. To calm down the notoriously rowdy ECW crowd, Kimona Wanalaya (later known as WCW's Leia Meow) voluntarily performed a long, "Seven Veils"-type striptease, until the ring could be repaired.

Theater

"Whatever Lola Wants" in Damn Yankees. Amazingly, Joe decides to Ignore the Fanservice.
And, of course, Gypsy.
"Ah, But Underneath" in Follies (used in some productions to replace "The Story of Lucy and Jessie").
The dance of the seven veils in Salome. In some productions, it goes all the way to full nudity.
"Take Back Your Mink" in Guys and Dolls, in which the Hot Box Dolls observe no distinction between "take back" and "take off."

Video Games

When you visit Votowne a second time in Anachronox, a reporter wants to schedule an interview with you, complete with a photoshoot. If the active member is Stiletto, he'll point out that he wants her to wear her beret for the shoot... and only her beret. If you have an other character active, the line is changed to include some other item that person wears, such as Sly's trenchcoat or Paco's cape.
There is a rather entertaining scene in A Dance With Rogues, in which the character can make a show of it while stripping for a minor character who won't help her unless she pays him or screws him. If you make a show of it, he "goes off" prematurely and performs the teleport you wanted him to in a fit of rage.
Heavy Rain: Madison is held at gunpoint and forced to strip tease for a skeezy nightclub owner.

Web Comics

Girl Genius: This trope was referenced in the background of the Jäger Bar in Mechanicsburg, where the Jäger impersonator girls are seen dancing on-stage without their trousers on, singing "But I've still got my hat!" This is a bit culturally significant, due to the importance of hats in Jäger culture.
The Web page for the Bonobo Conspiracy featured a "Site Traffic Strip-O-Meter". The more traffic the site received, the more clothes the cute girl removes, as explained in the FAQ.
Flipside: When Maytag has sex with on guy she does this.

Web Original

The Web newscast Naked News has stripping news anchors.

Western Animation

Stripperella. 'Nuff said.
Fablio le Magicien, an old animated series illustrating La Fontaine's tales (adapted from Aesop's) with anthropomorphic animals, had two episodes featuring a striptease (one by a female rat and one by a female bird).
Il giro del mondo degli innamorati di Peynet has a striptease performed by a girl in a series a psychedelic images accompanying a song, in the scene set in Britain.

Males