There was a 1980s anti-smoking advert on British TV where a group of girls are discussing how to chat up boys by blowing smoke suggestively. One tries it on a skinhead who coughs before answering with this line.
There was a UK ad for quick-cook pasta where a woman hears her annoying upstairs neighbour leaving his apartment. She rushes to put the pasta on and it's ready within a couple of minutes, so by the time he comes to the door and asks her on a date, she apologises and explains that she's just sat down to dinner.
Arcade Voice: [playing "The Big Score" game] Hey, big boy. Think you're man enough to score with me?
Jim Green: I am, if Bubba is.
Arcade Voice: Oops, sorry, tonight I gotta wash my hair.
Back to the Future Part II: Lorraine uses the line on Biff. Ironically she wasn't trying to let him down easy, considering she had just told him to "take a long walk off a short pier". At least Biff deserved it.
When Otter says that a girl broke a date with him in Animal House, Boon asks if she used this excuse. Subverted with Otter's reply - "Dead mother".
Gender Flipped by Lakewalker culture in The Sharing Knife. The woman is normally the one that makes advances, while the man is the one who has to come up with some excuse if he's not inclined to her.
Live Action TV
The Prisoner: Oddly enough, this is Number 24's excuse when Number 6 calls her for help in "The Schizoid Man." She comes anyway.
In Help Im A Teenaged Outlaw, Lady Devereux tells one of the servants in one episode (who is asking her out) that she will not be coming out with him because she is "washing her hair."
Played with on Dawson's Creek when Joey tells Dawson that if he can't find a date for a double date, he should call Jen and tell her he can't go out because he needs to "wash his hair"
In Kenan & Kel, after being rejected in the phone with this answer, Kenan suddenly remembers that the girl he was asking is bald.
Mash: Colonel Blake once put the moves on a nurse. He complimented her on her scent, to which she replied, "I just washed my hair." When the colonel goes a little further, she brushes him off with, "I have to wash my hair."
In the episode where Kelly Kapowski didn't want to go to the prom with Zack because she couldn't afford a dress, she used this one so often Zack told her she'd caused a drought in California.
The Big Bang Theory "The Cushion Saturation", Penny tries to excuse herself saying she needed to wash her hair to save herself from Sheldon's wrath when he was about to discover his self-designated couch cushion had been disturbed.
An episode of Diff'rent Strokes had Willis' girlfriend blow off a date with him by saying she had to wash her hair. He goes to the movies anyway and sees her there with another guy.
In the extended Glee pilot, Emma pulls out several of these excuses (i.e. "I'm allergic to nighttime") to discourage Ken from asking her out.
How I Met Your Mother has a cast-wide version. One character wants to get out of something unpleasant and she says she's washing her hair. Another in the group says "running the water," the third says "holding the towel" and the fourth simply says that he'll be at home, trying to cope with not being invited to the hair-washing party.
Lucille Ostero tells Gob "I have to go to spin class." Lucille has vertigo.
When Michael drops by Sally Sitwell's work to ask her out, he sees her facing away from the front desk in the next room. When he asks the receptionist to get her attention, she makes a phone call, then tells Michael she's not there. After Michael leaves dejected, it's revealed that the figure in the next room was simply trying on a wig that looked identical to Sally's hair.
In the second Bottom Live show, Richie tells Eddie to invoke this after he gets an invite to meet with "Mr. Big". Eddie points out that he doesn't have any hair.
In I'm Alan Partridge, Alan casts around wildly for an excuse to leave the house of a swinger couple who want to have sex with him and comes up with "I've just remembered that my father is...still dead".
Relient K's song "Mood Rings" - "She likes you Wednesday, but now it's Friday and she has to wash her hair."
A different excuse in Kirsty McColl's "In These Shoes";
He said, "Let's make love on a mountain-top, Under the stars, on a big hard rock" I said "In these shoes? I don't think so"
...Also a direct subversion, since the next line is "Let's do it here".
Lily Allen's "Knock 'Em Out" is essentially a string of these, ranging from the girl saying she's getting married next week to claiming she has to go because her house is on fire.
Used in a Dilbert comic strip in which the titular character asks a girl out. She gives him this line and offers coffee at the workplace instead. Dilbert declines, preferring someone with "clean hair."
Clue for the Clueless gives two versions of this excuse: The first is vague but plausible, such as "I have 'plans' this evening", the second is specific and implausible, for example "I have to wax my cat", and is generally reserved for losers.
A Garfield book listed this line as a way for a girl to refuse a date offer from Jon Arbuckle, adding onto it "each one individually".
The others in that book would mention listing here if they didn't venture dangerously close to I Have to Go Iron My Dog lines, especially if one considered the many, many, MANY rejection lines Jon's received through the years...
A variant shows up in one of the Chick Tracts: The daughter of a man whose soul the angels and demons were fighting over gets sent to go wash her hair by a guardian angel so that her Christian friend would try to convert the dad while she waited for the girl to finish washing her hair (because apparently Jack Chick thinks that it takes hours).
Narrator: Larry said: Come play with us. We're digging a trench.
Bill Corbett: Susan suddenly remembered that she needed to wash her hair.
In the furry comic ISO by Vince Suzukawa, when the main character Cody Frost is trying to work up the nerve to ask his crush, Gentle Giant Doug, out on a date, his Imagine Spot comes up with various reasons why Doug might turn him down. This excuse is one of them.
Not played quite straight in South Pacific: Emile isn't around when Nellie sings "I'm Gonna Wash That Man Right Outta my Hair" and washes her hair on stage. (She does not "wash that man right out of [her] hair", as her very next number is "(I'm in Love With) A Wonderful Guy".) Lampshaded by her fellow nurses:
Nurse: Well, she sure washed him out of her hair!!
In Charly: A Love Song, the two leads are set up on an unwanted date by their parents. After leaving the planned (and boring) date at the country club, Charly (the girl) reveals that underneath The Ojou exterior is a Genki Girl who only need a Ferris wheel ride to bring her out. When she tries to drag Straight Man Sam (the guy) along, he replies:
Asking the Bowerstone hairdresser to follow you in Fable I will result in this phrase if she doesn't like you enough.
One Concerned strip has Gordon trying to ask out one of his female co-workers at the Combine Citadel out on a date, and she gives him this excuse. The catch here is that the coworker, who was a normal human in the previous comic, is now a transhuman Combine soldier instead.
Subverted in thisQuestionable Content strip, where Faye has a legitimate reason for having to wash her hair: bubble gum.
In The Inexplicable Adventures of Bob!, this is Molly's excuse for standing Rocko up for a date bearing in mind that Molly is completely covered with pink hair. "I had to wash my hair. All of it."
The Spoony Experiment: The Spoony One once reviewed a Klingon language instruction CD where I Have to Wash My Hair is said to be a perfectly valid way of dealing with an unwanted Klingon suitor. A disbelieving Spoony responds "Oh come on, if that's a pussy line on Earth, it's gotta be a pussy line on Qo'noS!"
In a flashback episode of the animated spinoffBeetlejuice, young Beetlejuice receives this blowoff from a girl he has invited to the prom. The girl is a skeleton with no hair.
Used against Dexter on the Freakazoid!! episode "Dance of Doom".
The Batman did it with the appropriately titled "Superman Story". Clark attempts to ask Lois to see a boring documentary film. She brushes him aside, claiming she needs to wash her hair.
Megas XLR "Dude, Where's My Head" When Jamie decides to break his Non-Action Guy role and do a flying leap off a parking garage roof his date protests. Saying "It's been great hanging out with you and all, but I've got to go home and wash my hair."
In Futurama, we discover that, sometime in the past, Leela told Fry she couldn't go out with him because she had to meet a ghost. She wasn't expecting him to believe it (he did), so she flipped a coin to decide if she should use the excuse or not. In an Alternate Universe, where coin-flips have the opposite result, their counterparts went out and are now married.
In The Simpsons, Barney announces to the bar that he has a date "with the crazy lady who's always yelling stuff in front of the drug store," and a dejected Moe sighs and says "she told me she was washing her hair tonight."
Parodied in Doug, where one of Doug's Imagine Spots shows Patty Mayonnaise presented with a Dating Sim-like choice between Roger, Doug, or washing her hair.
In SpongeBob SquarePants when Sandy says she'll tear a new one to the person who caused Clamu pain, to prevent her from revealing he threw a peanut at Clamu he says "I have to get my hair cut!" and Sandy Lampshades this by saying "Wait a minute Spongebob doesn't have hair!...or does he?"
The Venture Bros. has an episode where Dr. Venture is pursuing another date with Charlene, or Dr. Girlfriend, calling The Monarch's cocoon. When Dr. Venture calls yet again for Dr. Girlfriend, the Monarch yells flustered, "Tell him you're washing your hair, or something, I don't care."
In the My Little Pony: Friendship Is Magic episode "Party of One", Rarity uses this excuse to turn down an invitation to one of Pinkie Pie's parties. When Pinkie points out Rarity's hair looks clean to her, Rarity goes so far as to stick her head in a garbage can full of rubbish to get away with the excuse.
Rarity: See? Dirty.
In The Swan Princess, Odette tries to use the excuse not on the prince himself, but on her father to delay leaving for the prince's kingdom.
Odette: I haven't packed or washed my hair, and Father, I get seasick!
Keep in mind that when this excuse first appeared, it wasn't outlandish at all. Back in the days when women generally wore their hair very long and in elaborate hairstyles, and before such things as showers and hair dryers, washing one's hair, drying it, and then putting it back up was a major undertaking. It was a legitimate excuse then.
It remained a legitimate thing right up until the widespread availability of commercial shampoos and conditioners. Washing hair with plain soap leaves a residue, so it was wash, rinse, change the water and add a little lemon juice or vinegar (to remove the residue), then change the water again for the final rinse. Even when hair styles became generally shorter prior to/after World War II, it could still be a long and occasionally arduous process. See here.