Outsourcing Fate

The Powers That Be can't decide what to do with the future of the universe, so they ask the opinion of The Everyman protagonist.

The Hero is obviously not qualified for choosing the fate of mankind, at least by traditional standards, but the Powers That Be have a good reason to trust him. Maybe he is The Chosen One who is predestinated to have the correct choice, the Ridiculously Average Guy who somehow represents all of humanity's opinions, or maybe, a more personal Powers That Be simply finds him sympathetic.

So The Hero has to use his best intuition, and make a choice that will influence everything.

This whole situation is closer to the idealistic side of the scale, so usually the protagonist's choice will also be the more daring, fantastic, and optimistic option.

Compare to Humanity on Trial, when the humans have to convince the Powers That Be to accept their will, instead of themselves getting trusted with making the right decision.

Examples of Outsourcing Fate include:

Anime and Manga

In Planet Ladder, the Ditz main character is responsible for deciding the survival of planets. Towards the beginning, her mentor tries futilely to pound that into her bubbly head.
In Scrapped Princess, the sufficiently advanced god-program-thing, Mauser, asked Pacifica if it was really such a good idea to trap mankind in Medieval Stasis, because she started to doubt in it herself.
In The Disappearance of Haruhi Suzumiya, Nagato Yuki obtains a power that can completely rewrite the world, and she asks Kyon if she should use it or not.
- Subverted in the rest of the series, where the main characters, especially Koizumi and Kyon always try to guide Haruhi's reality warping instead of herself, but only because she is completely unaware of it.
Mokona's modus operandi in Magic Knight Rayearth.
The point of Mirai Nikki. Subverted in that God instead asks the opinion of some of the most mentally fucked-up individuals in the world.

Comic Books

In Lucifer, God, after exiting his creation without warning (thereby bringing about its slow decay), has Elaine Belloc and Lilith (both of whom started out human) plead their cases for and against preserving the cosmos.
In PS238, the Powers That Be, with the time-traveler Tom acting as its agent, needs to decide whether humans should continue to gain Metahuman Powers, or if superpowers should gradually fade and disappear into myth - until next time the choice has to be made. But Tom isn't the one who'll make the choice - he merely chooses WHO gets to choose, and he picks Tyler Marlocke, the only normal boy in the 'School for Metaprodigies'. In the end, while he gets to summon various acquaintances to get their opinion of the issue, it's up to Tyler to decide whether superpowers should continue to exist...
President Bill is about a man named Bill who was picked at random to be the President of the United States.

Film

The 2008 film Swing Vote is about a U.S. presidential election that comes down to a lone man's vote, and the candidates' attempts to win his support.

Literature

In the fourth Foundation book, the protagonist had to choose between a Galactic Empire, a different Galactic Empire ruled by Telepathic Spacemen, or Instrumentality. He was chosen because he was statistically proven to be the luckiest person in the Galaxy.
- However, the prequel Foundations Triumph throws this into question when Hari Seldon deduces that R. Daneel Olivaw will hand-pick the most lucky man to avert a robot civil war.
The Night's Dawn Trilogy ends in this way, with the hero being granted the power of a "Machine God" to solve the problems.
In one of the Hitch Hikers Guide to The Galaxy books, it turns out that the real President of the Galaxy is a little old man in a shed in the middle of nowhere. All he's interested in is feeding his cat, but occasionally people stop round and ask him what he thinks about certain things.
The Isaac Asimov short story, Franchise, where elections were done, not by asking everyone one question ("who are you voting for?"), but by asking one person a whole bunch of questions (mostly unrelated to the election itself) then inputting all the answers into a computer and calculating the election results from it. Apparently the computer was so powerful that it could extrapolate national trends from a single person, but it needed that one "everyman"'s opinions to base its calculations on.

Mythology

There are several examples in Greek Mythology. Typically, there's a Sore Loser and a Curse, with the standard moral "smart mortals don't get involved with godly disputes."
- King Midas was asked to judge the music competition between Apollo and Pan. An angry Apollo gives him the ears of an ass when he rules for Pan.
- Tiresias was asked by Zeus and Hera to judge whether the man or the woman receives more pleasure from sex, as he'd been both. He chose women, and Hera struck him blind, for which Zeus compensated him by giving him prophetic powers.
- The Athenians were asked to choose a patron god by judging a contest of boons between Athena and Poseidon. The chose Athena's olive tree over Poseidon' saltwater spring, hence the city's name.
- Paris was chosen to select the most beautiful goddess among Hera, Athena, and Aphrodite. We all know how well that ended.

Video Games

In Ben "Yahtzee" Croshaw's homemade adventure game "Adventures In The Galaxy Of Fantabulous Wonderment" this happens at the end when the Powers That Be, actually the spirits of everyone who ever died, ask the hero to choose whether they should raise everyone to the same state of existence as them and explore other universes, or whether they should just let humanity develop on its own.
A notorious mission in Mass Effect 2 revolves around this. The Geth, a race of robots, have split into two groups - the main group, which just wants to be left alone to evolve and learn. A smaller group (aka 'the heretics') have taken up a deal with a race of Eldritch Abominations to recieve great power by becoming slaves. The main Geth have a virus that can rewrite the heretics to conform to the main group's point of view - effectively brainwashing them - and give them the desire to return home. The moral conundrum is whether to brainwash the heretics, or simply destroy them. The entire Geth race is divided almost exactly fifty-fifty over it, so they turn to the only organic they trust (Shepard) to make the decision for them.
This is how the world is supposed to work in Shin Megami Tensei Nocturne. Humans with strong Reasons (principles, really) fights each others and the victor ascend to Kagutsuchi, which then remake the world according to the Human's wish. But then Lucifer screwed the system by creating the Demi-Fiend (you, that is).