Wild Magic

The underlying magical forces at work in the universe, or at least in this section of it, are, quite literally, alive. And more often than not, they are completely amoral. At best they are whimsical, in a way that would normally be completely harmless. They just want to play. (Speaking of which, the dire wolf over there also just wants to play. We advise you go play with the dire wolf. It's safer, trust us.)

But if you are not so lucky, you may trip over a sentient magical force that wants something. Maybe it's hungry, and wants to eat your soul. Or maybe it's lonely and tries to get you to stay a while. You know, just for a few eternities. Not to be confused with cases where someone either gets lost in the underlying magical fabric of the universe all on their own, or decide they like it there so much there that they're staying.

Casting a spell with this kind of magic is often extremely dangerous. You have either have to convince magic to do what you want it to, subdue it in a battle of wills, or accept that you are basically tilting the metaphorical pinball machine of reality. Another danger of using wild magic to cast spells, generally more prominent when using methods 1 or 3, is a Heroic RROD. New users may also Go Mad from the Revelation.

Particularly powerful Wild Magic may take the form of Background Magic Field that renders reality unstable. Or, in other words, reality is a Reality Warper. It will frequently mistake your mind for a set of inspirational prompts. Think happy thoughts.Think happy thoughts very, very, hard.

Contrast Ritual Magic, where the casting and effects of magic are very rigid. Compare and contrast Magic Realism, which on the one hand treats magic as having a life of its own but also makes it subtler and/or weaker.

Examples of Wild Magic include:

Anime and Manga

Most magic in Slayers is either rule magic or theurgic, but Lina's Dangerous Forbidden Technique is wild magic. The Giga Slave is a version of a powerful theurgic spell, modified to call upon Chaos itself. As Chaos is both powerful beyond everything, and more than a little chaotic, there's the minor problem that a miscast Giga Slave could destroy the entire universe. Or not. The Lord of Nightmares is a very capricious being, and her mind always follows her power, so it really all depends on how she's feeling.

Literature

Enemy Glory: very active in the North Country, where reality seams to be on a constant quest to turn into the most grandiose metaphor for itself that it can come up with.
The Last Unicorn: Schmendrick's quest is to learn to use his magic. He can't make it do a single thing, but he can let it do what it wants ... which has some surprising results.
Forest Kingdom: oh boy. Not only is it alive. It wants the world as its playground. The first book is about trying to stop it. The second culminates in going into the world where the embodiments of magic live and then going on a killing spree
Greenwitch, the 3rd book in Susan Cooper's The Dark Is Rising series. The title creature is part of the Wild Magic, a force apart from (but equally as powerful as) the Light and the Dark. It's possible for others to control it, but attempting to do so is extremely dangerous.
Discworld - in general, but especially in areas which suffered a direct strike in the Mage Wars, such as that around the Wyrmberg. Generally, the higher the amount of magic in an area, the more likely it has a personality of sorts ... and probably not an especially nice one.
All magic in The Death Gate Cycle draws from the Wave of Possibilities, or Omniwave, which is also the force responsible for maintaining the universal balance. Normally the Wave affects individual spells very little, except to correct small flaws in them so they work, but in order to maintain balance it can cause the most powerful spells to have... interesting (and opposite) side effects. For example, any time someone is raised from the dead by necromancy, somewhere else another person will die untimely.
Daine from the Tortall Universe uses Wild Magic, which could also be called 'animal magic' because it lets her shapeshift and talk with animals. It doesn't quite fit the above description, but it's explained as a genetic ability from her God of Hunters father and overusing it can cause regression to a primitive state of mind, at least in the first book.
Circle of Magic gives us academic magic and ambient magic, ambient magic being a little more like wild magic. Academic magic is more Ritual, but ambient magic taps into the magic of the world itself and manifests itself in activities, such as cooking, weaving, gardening, sheer nothingness, and the weather. For particularly powerful mages, this can turn into Blessed with Suck.
The Dresden Files has Demonreach, a sentient island somewhere in Lake Michigan that you can only arrive at if you mean to and which actively opposes people who try to settle on it.
- Hell, most magic. In the Dresdenverse, magic (alongside physics) is the fundamental building block that the universe is built upon. Sure, humans and various supernatural entities can draw upon magic (including using Ley Lines), and channel it to their will, but it's still wild.
Tales of the Five Hundred Kingdoms has the Tradition, which pushes people who are susceptible to it into the paths of traditional fairy tales—the heroine of the first book is a Cinderella whose destined prince is still a child. If the magic of the Tradition can't be channeled into a tale, it simply accumulates around the person until someone decides to take it... or until the circumstances are changed until they no longer fit the story.
In the Chronicles of Thomas Covenant, Wild Magic (channelled through white gold) is the only force powerful enough to destroy the Arch of Time. Naturally, Lord Foul spends the first two trilogies trying to get his hands on Covenant's white gold ring.
The Old Kingdom Trilogy uses both this and Ritual Magic, though the latter is used much more often than the former, due to Free magic being extremely dangerous, as described in this trope. This actually ties into the main plot; originally, Charter magic didn't exist, but seven of the nine great spirits who created the world sought to create something more organized, and bound Free magic using the Charter. This was then used to organize and create the known world.
Rather obviously foreshadowed in A Sudden Wild Magic. Zillah, a mage with little to no self confidence, has been constantly referred to the Arth mages of what amazing power she has, and also fittingly has no control of it. It comes to show when she manages to teleport Marcus, Josh, Philo, and herself out of Arth and into Petarchy.
In Laura Anne Gilman's Retriever series the use of "current" borders between Force Magic and Wild Magic. Over use of it runs the risk of "wizzing out" which results in a mage that is both extremely powerful and completely insane.

New Media

In Descendant of a Demon Lord demons have a power supposedly stolen from the gods called "domain". This power has a mind of it's own and often drives demons to do bad things, which they can resist. Demons that live long enough (and demons are The Ageless) will inevitably permanently lose themselves to their domain and do what their domain tells them too. The protagonist is normally good about holding domain in and even then she is constantly leaking it. After a demon dies, that demon's domain tends to pass on to a demon blooded relative, turning the demon blooded into a proper demon.

Tabletop RPG

The Warp in Warhammer 40,000': Some people can harness it, but it's very dangerous for them and others.
Dungeons & Dragons
- Eberron features the Mournland, which used to be one of the most populous countries in Khorvaire until a magical disaster befell it. One of the common features of the landscape is living spells—ambulatory fireballs, crawling cloudkills, self-propelled acid arrows...
- The Forgotten Realms had Wild Magic Zones, where magic sometimes backfired on its caster or had some other weird effect. Also, mythals (elven large scale spell fields) can take damage and start unraveling, and then the place usually has a few wild magic zones and the entire area has some intended effects still working, some not, and some dangerously warped; for a simple example (decayed almost completely):

The mythal acts as a wild-magic zone by day and a dead-magic zone at night, and any healing spells cast within its area instill mummy rot rather than healing.

- 2nd Edition had Wild Mages who could control (O.K. somewhat control) wild magic.
  - As illustrated in Champions and Heroes (only slightly exaggerated).
  - Which returns in 3.5 Complete Arcane as a prestige class.
- By 4th edition it is a power/spell source for some sorcerers, it has different bonuses based on dice rolls.
The Mage: The Awakening Sourcebook Night Horrors: The Unbidden discusses how the magic that the Awakened use can go wild, especially when it is able to accumulate in one place (as a result of repeated spells or activity of supernatural beings, or for entirely unknowable reasons). It also talks about how such magic can spread, and the severe effects it can have.
GURPS Fantasy II. The strange effects on magic cast in the Madlands.
The Nightbane Supplement Through the Glass Darkly included rules for spells that had come alive and gained sentience. Later on this lead to aclass of Magic Users who deliberately did this everytime they caste a spell called the Spell Breather.

Webcomics

Roza's blood magic acts without her control.
Goblins has the magic item named the Shield of Wonder, which causes a random magical effect when being hit. Most of them are beneficial to the user of the shield (i.e. they harm the attacker), but are very often dangerous to him, too.

Western Animation

Young unicorns in My Little Pony Friendship Is Magic can run the risk, when very startled, of their magic going out of control. When Twilight Sparkle (one of the most powerful in recent memory) got her Cutie Mark, her uncontrolled magic turned her parents into houseplants, turned a baby dragon into a giant dragon, and came close to leveling the royal palace. Baby unicorns are even worse in this regard, since their magic is purely instinctive.