There's nothing hotter than feeling your spaceship throb beneath you as it switches into FTL drive. Same goes for the smooth metal touch of a car. Want to get busy with your machine? Here's a list of people who have.
We all know that something special transpires between people and their cars. But sometimes, when that car has its own personality, that bond can get - well - kind of naughty. Let's just say that the scene in Transformers where Shia and Megan making out on top of Bumblebee pretty much screams threeway. Bumblebee is even playing love songs.
And then there's the bromance of Knight Rider, which may not be sexual but is still . . . kind of gay.
In the J.G. Ballard novel Crash, and the amazing David Cronenberg film adaptation of it, we follow the exploits of a strange group of people who fetishize car crashes. The main way they get off sexually is to reenact car crashes they've experienced, or that famous people have died in. Here are two creepy/wonderful moments from the Cronenberg flick, where a character whose legs have been mangled in a car crash gets sexy with cars (and with people in cars) that remind her of her trauma.
But cars are just a pale imitation of the real deal: The spaceship. In Ken MacLeod's novel Newton's Wake, we meet a character named Lamont who has been having a romantic relationship with his spaceship, the Hungry Dragon. Eventually he falls in love with a woman named Higgins, a "rapture fucker" whose hunt for post-singularity technology led to an accident in which her head was replaced by a metal nanotech structure.
The main character in Charles Stross' Saturn's Children is a sexbot named Freya, who is programmed to have sex with everything, including furniture. In one memorable scene, she has sex with a device that is designed to sling her out of a planet's gravity well and onto a ship.
In the Culture novels of Iain M. Banks, ship Minds, which occasionally reside inside Orbitals (artifical ring-shaped environments in space), create humanoid avatars which interact with people - and sometimes have sex with them.
In Futurama, Bender and the Planet Express ship have a fling in the episode "Love and Rocket." Eventually Bender cheats on the ship, and she gets really stalkery and HAL-like. Fry and Leela have to go inside her control center, ala 2001, and alter her personality so that she'll stop going into jealous rages over Fry.
There are several novels which deal specifically with the romantic and sexual bonds between women and starships. Julian May's Saga of Pliocene Exile, published in the 1980s, explores a world where women can enter into "mind-marriage" with starships. Along similar lines, Norman Spinrad's The Void Captain's Tale is a novel about ships powered by female orgasms. A classic of this subgenre is The Ship Who Sang, by Anne McCaffrey, which turns the usual tale on its head. In this novel, a disabled human woman's body is wired into a spaceship, which she controls. The novel focuses on her romantic relationships with two different men who are her "brawn" or mobile companions.
Probably the gothiest, most emo ship/human relationship is between the humanoid Crais and the ship Talyn in Farscape. In the second and third seasons of the show, the sentient ship Moya encounters her prodigal son, the heavily-armed ship Talyn, for the second time. Her son has decided to bond with Crais, an often violent and unstable man whom everyone is worried will steer Talyn in a darker direction. By the end of the season, however, it seems that Crais was good for Talyn after all, and has tried to prevent the ship from using its weapons. However, their relationship is doomed: The bond between the two has made Crais physically ill, and Talyn continues to have weird behavioral problems. And it's also a bizarre love triangle, since Crais is drawn to another human, which undermines his relationship with Talyn.
While nobody in the raunchy, awesome Canadian TV series Lexx ever explicitly has sex with the sentient, planet-eating ship Lexx, there is a lot of flirting between crew and ship. And some fondling of knobs.
In Star Trek: TNG, the episode Tin Man focuses on a hyper-sensitive Betazoid named Tam, whose telepathic powers are so strong that he finds it hard to be around most species - their thoughts simply overwhelm him. But then the Enterprise comes across an ancient, sentient ship which has been sending out psychic distress signals. In fact, it's about to commit suicide because it can't find other members of its species anywhere. Tam hears the ship's distress call, and bonds immediately with it because the ship's psychic powers blot out all the voices that Tam normally hears in his head. In the end, Tam and the ship fly off together to explore the universe as one, joined mind.
Though the dragon birds known as banshees that the Na'vi fly in Avatar aren't technological ships, they are certainly a biological equivalent of fighter jets. And the Na'vi create lifelong pair bonds with the banshees psychically, after joining their fiber optic cables together and flying them. So I think it counts as an outlier example of emotional bonding between humans and ships.