Mikuru Asahina from Haruhi Suzumiya is a Time Traveler who's assigned to watch over Haruhi to unlock the mystery about why it's now impossible to time-travel beyond a certain day.
Meta Knight acts as the Mentor for Kirby in the anime adaptation, and tends to act this way rather a lot of the time, often serving as Mr. Exposition. Although he and his henchmen do take the odd opportunity to display how Badass they are on a regular basis, Meta Knight seems happy to leave the problem solving to Fumu and the ass kicking to Kirby.
In Umineko no Naku Koro ni, Bernkastel takes this role for the first two games, but once Beatrice indicates that she knows where Bern's loyalties lie, she takes a much more active role. It may or may not be the same Bernkastel as in Umineko, but Frederica Bernkastel is The Watcher of the Higurashi no Naku Koro ni continuity, as she is the collective amalgamation of all past Rikas, and is responsible for plugging Rika into another kakera after Hanyuu invokes her power.
In Puella Magi Madoka Magica, Kyubey is the living embodiment of this trope. Despite being a Manipulative Bastard, his actions only indirectly influence the storyline, and he really cannot break the rules which are assigned to him (grant a wish to an up-and-coming Magical Girl, no matter how weird it is). Of course, this does not stop him from giving out Wham Line after Wham Line in almost every episode.
He's also one of the few examples to employ this trope somewhat malevolently, being the absolute king of Exact Words and You Didn't Ask.
In Zeta Gundam, Big Bad Paptimus Scirocco would like people to think he is this, as evidenced by his Catch Phrase "I'm merely a witness to history", but the truth is he's just a very good player of Xanatos Speed Chess and is content to make a move only when he has to.
Uatu the Watcher, a Marvel Comics character (introduced in Fantastic Four #13) who lives on the moon, watches everything in every comic, and occasionally pontificates to the readership about it. He always loudly proclaimed "Yes, it is I the Watcher, who is always watching, but must not interfere", roughly every other sentence as if people were going to forget it. Which to be fair is probably a valid concern because quite notably, in spite of this expression, he almost always ended up interfering anyway. A hilarious example of him actually not interfering comes when the Red Hulk, who punched Uatu while on his Villain Sue trip, appears about to die. Uatu shows up and tells him "Sadly I am forbidden to intervene" and stands there so he can watch him get sucked into a black hole. This character is the Trope Namer.
As Uatu is no doubt well aware, his mere presence is a degree of interference. Earth's heroes long ago learned that Uatu only shows up in person when something really big is about to happen, so just by allowing himself to be seen he gives them a passive warning without technically breaking the rules.
In Original Sin #0, new Nova Sam Alexander asks Iron Man and Captain America why Uatu watches everything. After a beat, Cap admits that they have no idea.
At the end of Original Sin, Nick Fury becomes Uatu's successor The Unseen, as punishment for his actions.
It helped that in some of his comic incarnations, the Phantom Stranger was an agent of the Lords of Order and it was his duty to intervene against cases where Chaos was involved.
The Spectre in Kingdom Come acts like this. His job is to witness the coming (possible) apocalypse, not to interfere with it (only to punish the wicked should anyone be left after said apocalypse). Pastor Norman McKay who accompanies him fulfills the same role (having been chosen by The Spectre to accompany him in his observations). Norman however refuses inaction; telling The Spectre that this would be as evil as those who brought the whole situation to happen, and steps in to stop Superman's Unstoppable Rage.
Marvel's New Universe has The Witness, a character who dies as a result of the White Event, but continues to exist as an intangible ghost. He is drawn to places where people are manifesting paranormal powers, but can only watch what happens, unable to intervene in any way.
Raiden in the first Mortal Kombat film is a watcher; he gives advice to the heroes, but the other Elder Gods will not allow him to directly interfere. In the second movie, Mortal Kombat: Annihilation, he gives up his godhood so he can take a more direct hand.
In C. J. Cherryh's Cyteen and Regenesis, this role is played by the first Ariane Emory to the second Ariane Emory by way of the messages she left in Base One.
In Teresa Edgerton's Celydonn books, Dame Ceinwen often plays this role - she considers it part of the responsibility of having great power that she must not interfere too much.
In the Discworld novels, both Death and Lu-Tze of the History Monks are constrained by rules that prevent them interfering with history, although both bend these rules considerably in certain circumstances.
And both at least have something to do in the world. While their meddling was sometimes provoked by actions of Auditors. They are truly supposed to do nothing at all but observe and register.
Terry Pratchett's other work, Strata has people who stay in cryostasis on a orbiting satellite and are only woken to record big developments on a planet below. The job literally takes thousands of years.
Astinus of the Dragonlance novels is The Watcher of Krynn. Rumoured to be the god Gilean (the God of the Book, of course) in human form, he's the only man on the planet who, according to Raistlin's time vision, is not dying. He spends all of his time recording the events of the world in (generally) unbroken sittings. This is even to the extent that he'll be writing things like On this morning, Caramon entered my office— before turning to the visitor. He has also unintentionally interfered in events — mostly through Time Travel, when a protagonist obtained and brought back to the present one of his books from the future. On that day there was only one recording in his book: On this day of Overwatch Rising, Caramon of Solace brought me a volume of Astinus's Chronicles. A book that I will never write.
Warrior Cats: StarClan take this attitude toward the living characters, believing that interfering directly with the physical world would make the living cats their "playthings". This hasn't stopped them from occasionally making their will very clear, such as when they cause lightning to strike a specific tree, causing it to fall over and create a handy bridge to an important island, while simultaneously killing off a traitorous warrior attempting to usurp WindClan's leadership.
Actually, there is no concrete proof that StarClan was responsible for the lightning strike. Some of the characters assume it was a message from StarClan, but StarClan never takes responisbility it, and for all we know, it could have been a freak lightning strike. It's more likely that StarClan wasn't responsible because they've never done anything that drastic before.
Animorphs: The Ellimist claims to be this at first. Later, it is revealed that although both he and his evil counterpart Crayak would love to be more proactive, they tie each other's cosmic hands. Every time we see one of them do something, the other has agreed behind the scenes to let them do it as a part of a compromise, because otherwise they could cancel each other out endlessly. The trick to making progress in their "game", for the Ellimist, is hoping that the Animorphs will have the right reaction to the limited help or information he is able to give them, and/or that Crayak won't realize the true significance of a "move".
Live Action TV
Future Hiro took on this role in Heroes when he told Peter to "save the cheerleader," and again when he told his past self how to stop the bomb.
The Watchers from Highlander are prototypical, being members of an organization who observed the conflict between immortals but were sworn to remain apart from it. And just like Uatu they're really really bad at that second part.
The series actually deconstruct the idea of an organisation charged with observing a hidden world- while some take it very seriously, most treat it like any other nine-til-five job. They have pensions and even vacation time; in one episode Joe reveals to Duncan that they don't know who beheaded a recently killed Immortal, because that Immortal's watcher took some time off for his sister's wedding.
The Ancients in Stargate. And if we say they don't interfere, we mean it. The number of times Ancients interfered in the plot can be counted on the fingers of one hand, and every time, the individual who did so was genuinely punished by the rest. On two occasions an Ancient has evaded punishment by sacrificing all their powers and becoming human, then using just their superior knowledge to interfere.
The X-Files has several people in Watcher-like roles (often emissaries of the Powers That Be, or those within the Powers That Be but secretly working against them, e.g. Mr. X).
The Watchers of Ghost Whisperer, who annoy Melinda with their inability to give straight answers.
Medium: Allison's dead father-in-law fits the trope. He also annoys Allison by not giving straight answers and inflating the danger of what will happen just to be on the safe side or teach a lesson.
Fringe: The Observer and his organization are a group of bald men with advanced technology and almost no emotions (or taste buds) who observe major events in history, but seem to be showing up more and more frequently in the present day (Once an Episode, to be exact). Their purpose is unknown; they may be time travelers, immortals, or interdimensional police. They do sometimes interfere by communicating with the main characters in order to prevent the two universes from destroying each other, but they justify it as righting previous errors.
The Time Lords in Doctor Who. Again, while they were officially supposed to never interfere, a lot of them were really bad at it. Notably, their doctrine of noninterference was largely self-imposed; they made that decision in the first place because they're almost all horribly corrupt, and the doctrine is basically there to keep them from screwing up and/or conquering everything else.
On Buffy, Angel shows up in the early episodes only to offer Buffy cryptic messages about upcoming threats. Despite their name, Giles and the other members of the Council of Watchers act more like Mentors, and occasionally fight demons themselves.
Played straight(er) in the movie, where there was only ONE Immortal Watcher, who has trained The Chosen One's for centuries. He was allowed to do so by the Big Bad, so that the Big Bad would have some entertainment every now and again. Of course, The Watcher DOES intervene to save Buffy's life, and shortly afterwards dies for it.
In Deus Ex, this role is played by different characters throughout the game.
Initially, The Watcher is Alex Jacobson, the computer guy at UNATCO; he drops out after the La Guardia mission.
Daedalus takes over the role at the beginning of the Majestic-12 sequence.
The G-Man from the Half-Life series. Although he might also be considered the Sufficiently Advanced Alien as well. Then again, as time goes on, it appears that he's becoming less and less of a Watcher, especially after the death of Eli. "Prepare for unforeseen consequences", indeed.
The mysterious narrator/ the Lord of the castle in Knights in the Nightmare is one. He implies that the entire world was created as an experiment into human nature.
Teo and Lippti from Radiant Historia, though they are allowed to give the hero advice from time to time.
Specifically, Teo and Lippti are permitted to tell Stocke anything they like, they just can't see any possible timelines until he's already created them with a decision, and thus can only coach him on where he went wrong. The one thing they are absolutely forbidden to do is reveal or even imply anything about the goals and identity of the Black Chronicle wielder to the holder of the White Chronicle. This frustrates Stocke's efforts, but they later reveal it also protected him, since it works both ways. When they break this rule, they can only provide oblique and obscure clues, and it causes them excruciating pain.
Philemon from the firsttwoPersona games is mostly this, limiting his direct actions to giving the heroes the power to summon avatars of their inner psyche and pressing the Reset Button when his Evil Counterpart manages to destroy the world. In the nexttwo games in the series, he simply lets his servant Igor do all the work.
Many simulation games have the player as this, to some extent. Some simply have the player input variables at the start and leave you to simply watch whatever you put into motion.
In the Thief series, the Keepers act like this for the most part, although they will get involved if the situation demands it. Since they are undisputed masters of stealth, even when they do get involved nobody realizes it, and very few outside their organization are aware that they even exist. Deconstructed in the third game, when the Keepers — more specifically, their Glyphs — are the problem. A rogue Keeper who became a twisted immortal monster through her abuse of Glyphs is the Big Bad, and the leader of the Keepers spends the entire game hampering Garret's progress before finally accepting that the Keepers have become too attached to the power of the Glyphs. Right before the Hag kills him, he tells Garret to activate the Final Glyph which ends the power of the Glyphs and with it the Keeper organization. At the very end of the game Garrett is the last true Keeper. Which is rather ironic since he spent most of his life rejecting that calling.
Hyrule Warriors: Cia, the Guardian of Time, was originally a straight example of this as she observed the various timelines of the Legend of Zelda series. Things started to go wrong as she became more and more enamored with The Hero as she observed the heroic deeds of his various incarnations, and became more and more envious of the various Zeldas. After being egged on by Ganondorf's corrupting influence, Cia abandoned her duty and raised an army to invade Hyrule to get rid of Zelda and take the Hero for herself.
Concerned referred to this behavior as a "G-Peep."
Homestuck has Doc Scratch. The audience does eventually learn that he has an agenda of his own, but he brings about this agenda by contacting a few people and giving them advice to nudge them in the right direction.
Gubaru from the web fiction serial Dimension Heroes often watches the progress of the Dimensional Guardians via his base tucked away in a pocket dimension, occasionally contacting them via their Guardian Bands to offer advice.
Parodied: The Galactic Inquisitor insists he's only there to observe but his presence is so loud and burdensome he just keeps getting in the way. Unique in that he didn't try to intentionally interfere (though his presence was certainly obtrusive enough to count as interference) and everyone else just tried to ignore him.
Subverted in that, according to the alien disguised as Rusty's dad, when he was done with his evaluation he would have destroyed the earth.
Bob Woodward and Carl Bernstein portrayed Deep Throat this way in their book All the President's Men, and the movie follows suit. Understandable, as Nixon was known to fire anyone who he even thought was against him; indeed, Woodward and Bernstein were so certain their contact would be killed they made it clear they would not reveal his identity until after he died. (Although Deep Throat, AKA W. Mark Felt, beat them to it.)