Intimate Haircut

I cut his hair myself one night
A pair of dull scissors in the yellow light
And he told me that I'd done all right
And kissed me til the morning light

—"Samson" by Regina Spektor

When you go to the barber shop/salon, you often get your hair cut in public, and by somebody who isn't really close to you. In other media, cutting hair can become very sexual, as well as reliving the pesky Will They or Won't They? feeling. Often, a woman is cutting a man's hair and is very intimate. Sometimes, it leads to more than intended, but definitely is one of the many intimate acts between two people.

Examples of Intimate Haircut include:

Anime and Manga

Nothing sexual happens, but in Full Metal Panic!: The Second Raid, Kaname giving Sousuke a haircut is played as a very intimate scene because of the level of trust it shows that Sousuke has in Kaname — enough that he falls asleep while she's cutting his hair.
In Gurren Lagann, Nia asks Yoko to cut her ruined hair after they share a powerful bonding experience. The Les Yay subtext in that scene is staggering.
In Kannazuki no Miko, Chikane is the only one who can so much as touch her lover Himeko's hair without making her freak out (caused by the latter's traumatic experiences in the past).
In The Tyrant Falls in Love, Morinaga finds out that Souichi doesn't like going to salons, and offers to trim Souichi's hair for him. As he's cutting it, he realizes that Souichi has several erogenous zones on his scalp, hence why Souichi doesn't want a stranger touching his head. Morinaga being Morinaga, he tries to take advantage of it and gets immediately pummeled as a result.
The first Fullmetal Alchemist anime gives us a variation: At one point Winry offers to braid the titular alchemist's hair; at first Ed waves it off, thinking nothing of it other than convenience, but her uncharacteristic insistence clues him in. It ends up as a rather heart-harming and promising little scene.
Pandora Hearts: Vincent and Leo have a lot of Ho Yay together. It's especially evident in one scene where Vincent cuts Leo's bangs for him and then touches his face.

Film

Phenomenon does it with George and Lace. Subverted, as they didn't do anything until much later in the movie.
The Incredible Hulk does it with Betty and Bruce.
Edward Scissorhands averts the trope when Joyce tries to seduce Edward as he cuts her hair.
Bourne cutting and dyeing Marie's hair in the 2002 film of The Bourne Identity.
Harry Potter and the Deathly Hallows - Part 1 has a scene where Hermione cuts Harry's hair; while their affection is brotherly and sisterly, Ron thinks it's this trope.
The Pierce Brosnan indie film The Nephew does this, overlapping with Important Haircut. Aishling cuts off Chad's dreadlocks in a very intimate scene.
Pretty much the whole point of Le Mari de la coiffeuse http://www.imdb.com/title/tt0100112/
Fergus and Dil from The Crying Game - in the beginning, it's Fergus getting a cut from Dil, with soft lighting and all that entails. After the infamous reveal he cuts her hair in a manner that is depicted as violent and distressing for Dil, even though it's to protect her from the IRA.

Literature

In Ru Emerson's The Princess of Flames, Archbishop Gespry is shaved regularly by his longtime lover Fialla; various people comment on the trust this implies.

Live-Action TV

On The Drew Carey Show, Drew's female barber (Jamie Lee Curtis) straddles him while cutting his hair. They have a thing for an episode or two.
In one episode of Friends, Joey's girlfriend (on whom Chandler has a huge crush) offers to cut Chandler's hair. It becomes quite intimate, particularly when she runs her fingers through it to check whether it's even, and they end up kissing.
Beard version on CSI: the "Do you trust me" scene between Sara and Grissom where she shaves him.

Real Life

This trope is inverted in Real Life by people who have a haircut fetish/kaldari. Unnoticed in Western culture, as to such people haircutting is erotic rather than leading to possible arousal.