Heads or Tails

Alice needs to decide between buying a strawberry cake or an apple cake, but she really can't make up her mind. So, she tries to decide by...flipping a coin. Heads, strawberry. Tails, apple.

Flipping coins to decide on an action has been a practice that, according to The Other Wiki, dates at least back to Ancient Rome. In fiction, it usually happens in the following situations:

A character is unsure whether the option they are considering is the correct one, so they leave it up to fate.
The Powers That Be dictate what action must be taken.
A third party is trying to solve a dispute between two other people or factions. Often happens in contests when there is no clear winner.

Note that this trope can be used when deciding between two characters, things, or virtually anything.

A Born Lucky character will almost always get the result they want in this. A staple feature of The Gambler and The Trickster, who frequently settle their disputes this way. Cheaters tend to use a Two-Headed Coin. Heads-Tails-Edge is a subtrope.

Examples of Heads or Tails include:

Anime and Manga

In Hunter X Hunter, members of the Spiders flip a coin to settle disputes.

Comic Books

Two-Face's signature item in Batman is a double-headed coin, except one side is all scratched up. This allows him to easily identify which side landed.
In a Donald Duck story by Carl Barks, "Flip Decision", Donald is conned by a charlatan into believing in Flipism: the idea that all of life's choices can be made on the flip of a coin. Hilarity Ensues, of course, though the coin does show uncanny predictive power.

Film

Mr. Tako habitually does this in King Kong vs. Godzilla to make decisions. He even does it when the two monsters first confront each other in an attempt to predict the winner.
In Scarface, Guino Rinaldo was the one to popularize this trait as a quirk of gangster and gangster movies in general.

Literature

This happens twice in The Mote in Gods Eye.
- While the midshipmen are trying not to be captured, Horst Staley proposes flipping a coin when deciding what to do so his Mediator Fyunch(click) can't predict his decisions.
- When the human expedition prepares to leave the Mote system, the Moties send them a gift ship full of alien technology. The human leadership decides to randomly cut up the technology into pieces in case the Moties designed any of it for nefarious purposes. While Lady Sally is directing the procedure she flips a coin to decide how many times to cut.
No Country for Old Men: The main villain flips a coin to decide whether to kill a potential victim. Those that choose not to take the chance are killed anyway, because they refuse to submit to the Powers That Be.
In the book Q and A Ram flips a 'lucky coin' to make important decisions throughout his life. As it turns out, Ram's coin was a trick coin and he was fully aware of what life-changing choices he made throughout the story.
From The Stainless Steel Rat:

I flipped a coin to decide, and of course won since I had palmed the coin before the toss. It was going to be action.

Isaac Asimov wrote a short story called "The Machine that Won the War", where the final reveal is that a war has been won this way.
In The Wheel of Time books, Mat, and sometimes Rand, uses this method to make decisions. Since they both have luck-bending reality powers, this has extra significance. Mat in particular has a tendency to get coins landing on their edge.

Live Action TV

Frequently used to settle haggling debates on Bargain Hunt when the team's expert and the seller cannot agree a price.
The series finale of JAG ends with Harm and Mac (who finally tied the knot) flipping a Challenge Coin to decide which of them will leave the military and live with the other so they don't have to be stationed apart from each other.
The Mentalist: An episode of season 2 features the protagonist winning a bet this way. It landed heads 20 times in a row. No wonder they thought he was cheating.
In an episode of Scrubs, J.D. and Kim can't decide if they want to keep their baby, so they leave it up to a coin toss. It lands on its edge.

Sports

In international soccer/football, the referee does a coin toss with the captains of both teams before the game. The winning captain decides which half of the field his team will defend, and the other team kicks off to start the first half.
In American Football in general and the Super Bowl in particular, a coin flip decides who gets to choose one of the following first: which goal to defend and whether to kickoff or receive. The winner usually decides to receive and the other team gets to choose which goal to defend; but sometimes the winner will decide which goal, leaving the choice to receive or kick to the loser. At the start of the 2nd, 3rd & 4th quarters the direction of play reverses, and at the top of the 3rd quarter whoever received at the beginning of the game now kicks off. If there\'s overtime they have another coin toss.

Tabletop Games

Magic: The Gathering has a few cards that require you to flip a coin.
This is very common in the Pokémon Trading Card Game. Each player has a coin of his or her own. Players flip to see who goes first. Then there are several cards where the player flips his or her coin to determine the number of cards they draw from their deck or the amount of damage a move will do etc.

Theatre

Played With in Rosencrantz and Guildenstern Are Dead. They periodically flip a coin to make a decision, but it is established early on that the coin always lands heads up, as a symptom of You Can't Fight Fate. Until the one time it's tails.

Video Games

Dante picks up this quirk in the second installment of Devil May Cry for unexplained reasons, using his coin to determine whether or not he'll help Lucia and Matier, most notably when deciding who between him and Lucia will go into Demon World and slay the recently-revived devil king Argosax and most likely be trapped there for eternity. Lucia notices in the epilogue that it's a trick coin and the coin itself later comes in handy when Dante switches his own lucky coin with the Arcana Medaglia to fool Arius near the end of the game. Dante retains this trait during his guest appearance in Shin Megami Tensei III: Nocturne. Savvy players can actually recruit Dante for only one Macca if they know about the trick coin.
In Final Fantasy VI Edgar and Sabin flip a coin to determine who will be king of Figaro. Edgar won, by using a Two-Headed Coin, in order to not keep the burden off his brother's shoulders. Later, Celes borrows the same coin against Setzer. He falls for it.

Celes: Heads, you take us to the Empire's capital. Tails, I agree to marry you.

Web Comics

Played with in Homestuck. Terezi will sometimes make decisions with a coin flip. (The coin is two-headed, but one side is scratched) However, she more often than not ignores the result and just does what she wants.

Western Animation

In an episode of Futurama , the main characters enter an alternate universe where coin flips have opposite results causing decisions to be different.