Sympathetic Magic

In order to perform magic on an individual, you need to (or will have a much easier time if you) have a part of them. This may be a physical piece (hair, nail clippings), a possession, photograph, or just a unique description of the subject.

Compare I Know Your True Name, where the thing you need is (surprise!) the subject's name.

A variety of Functional Magic.

Examples of Sympathetic Magic include:

Anime And Manga

In Soul Eater, Tezca Tlipoca can track anyone whose soul he reflects in his mirror.

Film

In Drag Me to Hell, after being denied an extension on her mortgage by loan officer Christine Brown, the gypsy Sylvia Ganush rips a button from Christine's coat, using it to put a curse on her that will, well... honestly, just look at the title.

Literature

In the Immortals quartet by Tamora Pierce, Numair finds Daine using a "focus" made out of a lock of her hair.
Evie Scelan gets her hair chopped off so that the Bright Brotherhood can use magic on her.
Discworld:
- Hogfather uses this in the extreme. The Tooth Fairy originally began gathering teeth from human children to prevent them from being used for sympathetic magic. However, as they were all gathered in one place, it made them a perfect target for an assassin who intended to use said magic to make the children of Discworld stop believing in the Hogfather in order to kill him... It's a long story.
  - It's also mentioned in Hogfather that Wizards collect and burn loose hair and toenails to prevent Sympathetic Magic from happening.
  - Sympathetic magic itself is described as "old magic", so old that it's not even proper magic any longer.
- Also, played with in Witches Abroad, where Voodoo is compared to mirror magic.
In Robert A. Heinlein's Magic, Inc., that kind of magic (along with every other kind ever) is mentioned when the protagonist is warned to guard his hair and nail clippings, etc. As I said, every other kind of magic is also either mentioned or implied to also work.
- Harry Dresden also takes special care to collect his own toenail clippings, even though he does it in the privacy of his well-fortified apartment.
- In the Operation Chaos novels (which are a Homage to Magic, Inc.) it is the same, all kinds of magic work.
DNA (and/or RNA) in science fiction stories works as Sympathetic Magic.
The two Principles of Thaumaturgy (the first magic) in Lyndon Hardy's Master of the Five Magics are:
1. The Principle of Sympathy: Like produces like.
2. The Principle of Contagion: Once together, always together.
Gaining a part of a person allows you to use magic on them from a distance in The Dresden Files. When Harry gets knocked down and attacked in the first book, he's mostly concerned about the fact that the assailant took a clipping of his hair. In a later book, after a brawl, Harry's relieved when Charity Carpenter knows to burn all the gauze and bandages with his blood on them.
The Island of the Day Before by Umberto Eco, one of the characters attempts to use sympathetic magic to solve The Longitude Problem.
In Orson Scott Card's "Alvin Maker" series, Peggy, the torch who watches over Alvin uses his birthing caul (the amniotic sac from his birth) to use magics to protect him as a child.
One of the main forms of magic practiced in The Kingkiller Chronicle, along with naming. The physical properties of sympathy are well defined, following the Laws of Correspondence, Consanguinity, and Conservation. The more similar two materials are, the stronger the link between them; two objects that were once one object have a stronger link; and energy is neither created nor destroyed in the sympathetic process. The result is that even if you had a person's hair, you'd still have to have rigidly-trained focus and a great deal of energy to do anything to them.
Harry Potter: Polyjuice Potion allows the drinker to transform into somebody else, if they happen to have a strand of hair or some such from that person to brew into the potion.

Live-Action TV

In one episode of the horror anthology series Monsters, the rather slimy Corrupt Corporate Executive Villain Protagonist is concerned that his use of voodoo magic to get a leg up on his business rivals has made him the target of a demon named Obeya. Unnerved by the repeated hauntings of the voodoo priestess he partnered up with (who turned out to be one of The Undead all along), he invites the night janitor into his office for a drink. The janitor happens to be an expert on the occult and tries to comfort his boss. The janitor explains that 1) "demons only go after bad people" (see Villain Protagonist above), 2) "you have to invite them in for a good time, kind of like how you invited me in for a drink", and 3) "they need a piece of you" (the man had earlier donated some blood for a voodoo ritual). Meaning the first and third conditions had already been met. Since the janitor was actually Obeya in disguise, so was the second one.

Tabletop Games

Mage: The Awakening has a series of modifiers for using magic at a distance, ranging from "you barely know the person or location" (damn near impossible) to "you know the person/location well, and have a personal belonging/a piece of them" (relatively easy). The two most significant modifiers to sympathetic magic are a person's belongings (or for locations, something from there) and their true name.
In Unknown Armies rituals and Tilts (sort of a makeshift ritual) usually require something from the person you are trying to affect. (For bonus points it's good to have their name too)
Ritual Magic in Shadowrun can be performed via personal belongings in lieu of being able to see the target. The more closely related to the target the item is, the more likely the spell is to hit. As a result, Runners hate to leave anything behind.
- It should also be noted that not only is Ritual Magic more powerful than regular magic (thanks to the multiple casters), but any spell can be cast via ritual magic as long as all the casters know it. If you're lucky, you might just get a Detection spell cast on you. If you're unlucky, you might be the target of a "Slay [Metatype]" spell. If you're really unlucky, then you'll become the focal point of a Force 20 Powerball. If your GM uses Ritual Magic to cast Orgy on you, then you've got a whole 'nother series of issues going on that I don't want to deal with on a family site.

Video Games

Monkey Island, which uses voodoo as stated above.
In Shin Megami Tensei: Devil Summoner - Raidou Kuzunoha VS King Abaddon, a Skill-order demon's ability to disguise Raidou as someone else requires a lock of the target's hair to work.

Western Animation

In The Simpsons episode "Praiseland", the eponymous family are helping Ned clean the house from thing that remind him of his late wife Maude, Bart takes Rod's first tooth to use in magic.