Dramatic Dislocation

A dislocated joint, usually a shoulder, is a fabulous dramatic device. It's (usually) non-lethal, it hurts a lot, it disables full range of motion, and the character is usually forced to reduce (relocate) the joint without the convenience of proper medical attention or anesthetics, meaning it will almost always hurt. A lot.

The injured person will often have to coax someone nearby into assisting with the reduction, which they will be reluctant to do because of the Squickiness of the procedure. The opposite of this is when the injured person is assisted by a more experienced individual who lulls them into a more relaxed frame of mind before surprising them with the burst of pain when the joint snaps back into place. If you want to show someone as a total Badass, have them reduce their own shoulder by slamming it into a wall.

This trope has some elements of Truth in Television; while it is always better to seek proper medical attention, people in remote locations such as hikers and skiers sometimes have to reduce dislocated joints on their own. Where this trope starts to break from reality is the method used to pop the bone back into place. There are procedures that, while not as quick and dramatic as those shown in media, can put a shoulder back into joint with minimal pain, and most people with experience dealing with injuries would know this.

Examples of Dramatic Dislocation include:

Anime & Manga

Alex Armstrong in Fullmetal Alchemist has his shoulder dislocated by the homunculus Sloth. After taking a beating due to having only one working arm, he uses Sloth's attempt at a finishing blow to pop it back into place, turning the tide of the fight dramatically.
In Mobile Suit Gundam Wing, Heero Yuy dislocates his knee after failing to open his parachute in time after jumping out of a building. He later pops it back in place with considerable pain, given his established badassery, and with an exasperated remark from Duo who is disgusted by the act.
In the last episode of the Ultimate Muscle anime, Kid Muscle/Mantaro's shoulders are dislocated by Kevin Mask during their encounter in the finals of the Chojin Olympics. While he's eventually able to pop them back into place simply by flexing his arms (that's how muscular he is), he later dislocates them again intentionally to escape Kevin's Big Ben Bash.
Clare from the Claymore manga dislocates a shoulder during her training, and pops it back in by ramming her shoulder into a wall.
Ginji of GetBackers fame once had both arms and legs dislocated as a form of non-lethal restraint. He proceeded to pop one shoulder back in by hurling himself on the ground hoping it would hit right. Somehow, it did, and he then leaped out the window of the boat. Cue comically trying to swim with only one limb.

Comic Books

Spider-Man once did this in order to put a dislocated jaw back into place after battling Hammerhead. Proportionate strength of a spider + metal garbage bin = ow.

Film

In The Chronicles of Narnia: Prince Caspian, Edmund does the surprise pop-in after Peter dislocates his arm.
Martin Riggs of Lethal Weapon can dislocate his shoulder at will, and uses it to escape from straitjackets and ropes. Of course, afterward he has to pop it back in place (by himself). The fact that he does both of these things without doing more than grimacing serves to underline Badass he is (though he does cry out in pain when he reduces it, and he cringes and curls up into a standing fetal position when he's not in combat).
- Or how crazy he is.
Jet Li manages to pull off a relocation in mid kung fu battle in Fist of Legend. After fighting one-handed for a couple of minutes, and still holding his own. When he finally pops the arm back in, his opponent gets a mild Oh Crap moment.

Live Action TV

At least three times on Lost: Charlie reluctantly helps Jack, and Kate reluctantly helps Juliet. Libby goes for the surprise version in "The Other 48 Days" while telling the injured Red Shirt a story about skiing.
Dr. House once instructed a non-doctor in resetting Mira Sorvino's toe in "Frozen".
How George and Callie meet on Grey's Anatomy.
Xena gets commented on a dislocated shoulder, and rams it against a wall to pop it right back in.
In one episode of Burn Notice, Michael lets the bad guy dislocate his shoulder (which Fiona chides him for later) to maintain his cover, then, after the bad guy leaves, slams his shoulder against a post to pop it back in. In the next scene, it's clearly still sore, and not helped much when the same bad guy threatens to dislocate it again.
The M.O. of the martial artist A.I. Iron Schwartz in Real Drive is to dislocate the joints of his defeated opponents both to humiliate them, and to prevent them from continuing fighting reliably without putting their lives in danger, since it's implied that androids can't kill.
Claire of Heroes, has done this of course, due to her tendency to go get fatally injured at the slightest provocation. A particularly gruesome scene showed her popping in her shoulder joint—and also pushing her ribs back inside her chest.
Martha Jones in the Doctor Who episode "The Doctor's Daughter" popped in the shoulder of a Hath (a fish-like alien) immediately after it had been injured while trying to kill her. This earns her the respect and friendship of all the other Hath.
Faith uses a shoulder relocation as a segue into sex in one episode of Buffy the Vampire Slayer; notable because she uses the mild-mannered Xander merely as a counterweight.
In The Pretender episode "Keys", Miss Parker dislocates her own thumb in order to escape a set of handcuffs.
Ronon Dex from Stargate Atlantis, after dislocating his shoulder in an explosion that caused the space station they were on to start falling out of orbit, slams his shoulder into a wall to get it back into place. This despite Sheppard being right there, telling him to calm down and offering to help.
In an episode of Farscape, having had his shoulder dislocated in a fight, Crichton "pops" it back in by pushing it against a wall. A nearby villain, apparently omniscient due to hazily-defined "magic" powers, notes that Crichton did the same when it got dislocated after a motorcycle crash when he was in his teens.
On Angel, Doyle can do this with his neck. Being half demon helps.

Video Games

Metal Gear Solid 3: Snake Eater features Naked Snake getting, among other injuries, a dislocated elbow after he falls from a bridge. After using the proper medical tools on him, the player gets to watch him reduce the joint, complete with nerve-wracking sound effects.