In the fluff for Warhammer 40,000, the Space Marines in general are badass enough to be a One-Man Army to a man. That's before you get to the First Company veteran troopers, who can obliterate entire platoons or companies of regular troops. Then you get to Marines in Terminator armor, which is able to withstand being at the heart of a plasma reactor and getting stepped on by a three hundred meter tall walking battle cathedral without much damage. Then you get Space Marine officers and company commanders... and then Chapter Masters...
To say nothing of the Adeptus Custodes, who are said to be to a Space Marine what a Space Marine is to a normal human. And then you have the Primarchs, who function as the genetic template for all Space Marines, and above them, in his glory days, The Holy God-Emperor of All Mankind.
And above him... is Ciaphas Cain, HERO OF THE IMPERIUM! ...himself humbled by Guardsman Hawke from Storm of Iron, who wiped out about half of the Iron Warriors Chaos Space Marine force besieging the citadel. Sadly, it wasn't enough. He was the only Imperial survivor, though.
However, it is implied in other background sources, that some of the Marine's feats are just Imperial propaganda. Some fluff depictions have a single marine taking out entire armies of Mooks, others have marines struggling to go one-on-one with the very same Mooks. In much of the fluff Marines are deployed as companies and rarely decide the conflict alone. Others have them annihilating everything in their path.
This even occasionally reaches the point the same book doesn't even remain consistent. For example, Nightbringer has a group of Space Marines being butchered by a small group of Planetary Defense Force soldiers, which is more egregious when it is factored in that the planet in question was considered to have a poor PDF force by the low standards of the PDF. Later in the book, an even smaller group of Space Marines makes a good showing against something powerful enough to be worshiped as a god.
In general any named character tends to be this, giving the armies based around them the nickname "Herohammer" due to these characters being able to take on a literal army and still stand a reasonable chance of winning. Notable ones include Marneus Calgar, Abaddon the Despoiler, Mephiston, Njal Stormcaller, and Logan Grimnar.
Also, when you consider the fact that Space Marine augments can drastically increase their lifespan, and the amount of combat experience required to become a veteran or commander, most of them will have taken part in hundreds of years worth of campaigns, and could potentially rack up individual kill counts in the millions!
In Lord of the Night, Zso Sahaal drives a hive (VERY big city, VERY many people) into near-destruction before his brothers come to destroy the rest of the planet. Him being the First Captain and chosen heir of Night Haunter himself might have had something to do with this.
In Iron Snakes, A ship full of Dark Eldar crashes to a remote planet. The inhabitants' armies are butchered and everything looks very bleak... so they invoke an ancient pact to the Iron Snakes, who respond. By sending a single marine. The marine takes with himself a hunting dog and goes into the wilds. Oh, and he kills the Dark Eldar.
The biggest example of this are the C'tan, who are capable of destroying entire stars, but also want to eliminate all life from the galaxy and permanently separate the warp from real space.
C'tan are actual units in the tabletop game, costing almost 60% more than the next most expensive model in the game (the Land Raider battle tank), and capable of cleaving through multiple units by themselves. The creators have stated they're being removed from the next Necron update for being too weak.
The Grey Knights live, breath, and have exterminated daemons from this trope. They're the only group %100 immune to the Chaos, probably by eliminating the weak. They can devastate entire armies with just a few of them, and there's only about 1000 of them total. They're too small (by comparison) to be a Badass Army, but they qualify for Bad Ass Platoon easy!
Grey Knights are not immune to Chaos, this is a Common Knowledge misconception. They don't even have particularly special resistance to it (they are roughly on the same level as any Space Marine Librarian). They mostly have access to better equipment and have more experience against Daemons. The most likely explanation for the lack of Grey Knights falling to Chaos is the constant scrutiny they face by well educated peers. Most Librarians that fall in other chapters can easily conceal this due to the enforced ignorance of their chapter brothers. Grey Knights are constantly in proximity of Inquisitors and other psykers capable of recognizing the signs of the taint. Falling to Chaos is a lot less appealing when you will almost assuredly be killed the moment it is attempted.
Why has nobody mentioned Sly Marbo yet? Other Warhammer 40,000 characters may fit this trope, but Marbo explicitly has nothing else to his character BUT this trope! He even has an in-game rule which takes the name of this trope. Marbo is, of course, a thinly-veiled homage to every 80s action film hero and FPS character ever seen. He even looks suspiciously like Arnie.
The Eldar Harlequins. Using a variety of exotic and powerful wargear in conjunction with their incredible (even by Eldar standards) agility and grace, they kick just as much ass as the Grey Knights.
The Eldar Phoenix Lord Maugan Ra single-handedly defended a planet from an entire Tyranid splinter fleet. He also fought through the Eye of Terror during the 13th Black Crusade with the intention of saving his home craftworld Altansar. Not only was he successful in this goal, he also caused so much damage to Abaddon's legions that it rendered the Chaos forces impotent and was one of the main causes behind their eventual defeat. Do not fuck with this guy.
Canonically all of the Greater Demons in Warhammer, especially the Bloodthirster. In-game, a strong elite unit would have a reasonable chance of killing it. The Chaos Chosen One Archaon though, fits this well enough that a recommended strategy for fighting him is to try and shoot his Hellish Horse, and then stay out of his way until the game ends.
Though certain clever combinations of magic items could seriously damage a Bloodthirster, especially the Dark Elf talisman that effectively gives every wound inflicted on the bearer a 50% chance of actually working and a 50% chance of inflicting a wound on the person who hit the Dreadlord instead.
In the same game, Sigmar Unberogen (the founder of the Empire) was renowned for his strength and skill, least of all for defeating an entire army of evil creatures armed only with an animal's jawbone. It is, of course, a mirror of the biblical figure Samson, but as an individual it is canon within the Games Workshop history.
Related to Sigmar (possibly literally) is his Chosen, Valtan. Although now canonicaly dead (assassinated in his sleep) and not the best fighter ever, he had a rule that meant he almost always came back if you killed him, and attacked again. And again. And again. This could end with him racking a kill count that would shame Archaon. He became known to some as "Yo-yo Valten."
Looming majestically over Archaon, the Undead armies have Nagash. Previously a mere human, through magic and willpower he grew to such power that he eventually managed to single-handedly purge an entire fortress AND it's attached enormous subterranean dungeon of monsters in a single night, hours after having returned from the dead himself by sheer determination. That, and he is currently revered as the God of Undeath, so powerful that just the use of his name can draw blasphemous dark magic to the one who spoke it. In game terms, he was the only model (of hundreds) who began the battle as a level 5 Wizard, and was so powerful that he has been removed as a playable model and promoted to a mythological being in the newest edition.
Actually Nagash's magic level of 5 was neither innate nor unique - he derived it from a magic item (the Book of Nagash) and in the 4th-5th edition rules where he was available there were similar magic items that could make other powerful wizards level 5 also (the High Elf High Loremaster Teclis and Lord of Change Amon'Chakai were both level 5). He could still destroy entire armies by himself though, and in the background was responsible for the destruction of an entire civilization and (very nearly) the entire world.
The Venerable Lord Kroak of the Lizardmen armies. True to the trope in that even though he has been dead for thousands of years, his corpse is capable of leveling entire cities with godlike magic power. Physically, though, he is quite brittle and relies on magical enchantments to protect him.
Lord Mazdamundi is close to Lord Kroak in power, and is most likely one of the most (if not the most) powerful living mage in the world.
There was a tournament of champions style article in which the best special character from each of the warhammer armies of the time were pitted against each other. The Bloodthirster was used to make up numbers, since there were 15 characters, and 16 slots. The Bloodthirster rolled over everyone.
Dice for the Dice Throne!
Incidentally, everyone who took part in that very Tournament were all examples of this trope, however the semi-finalists in particular stand out. There was Archaon, the Chosen Warlord of Chaos Undivided, the Venerable Lord Kroak who is the most senior of the oldest and most powerful mortal mages, the Bloodthirster who is an incarnation of the Evil God of Death and War, and... Deathmaster Sniktch, a Ratman Ninja who was quite strong and had poisoned swords. Doesn't sound like much of a match, but when you consider that Sniktch had fought his way past people riding on dragons and the immortal Princes of the Elven race to get there, only to subsequently be written out of the next edition of the game for being too powerful...
In-game, sufficiently powerful wizards (Lizardmen Slann, Dark Elf Sorceresses, High Elf Wizards), dragon-mounted Elf characters (especially Malekith), and most other characters are sufficiently well-equipped and generally powerful to slaughter/blast their way through hordes of grunts.
There might be slightly too many of them to count here, but the unnamed High Elf spearman squad that pulled the most badass You Shall Not Pass ever recorded and held the gates of Tor Yvresse against an entire Goblin army without backup for three days before Prince Tyrion finally showed up with his dragon and some reinforcements to bail the last half-dozen survivors out.
No love for the orcs? Orcs only follow those who are able to beat them, or promise them a good fighting (and some how prevent them from beating you and taking over your army). Also they live to fight, so their legendary leaders are those whose actions are feared by all other armies.
Azhag the Slaughterer is not only a Black Orc Warboss on a wyvern, but also a lvl 3 wizard.
Or how about Gorbad Ironclaw, who removed an entire Imperial province from map?
And then there is Grimgor Ironhide, who lives for war. In 6th edition he gave combat resolution simply for being in combat. So if you did nothing and your enemy did nothing, the side with Grimgor would win.
Dungeons & Dragons sourcebooks generally describe the "ordinary citizen" as being a Level 1 Commoner or Expert (depending on if they're a peasant farmer or a skilled tradesman), and even soldiers aren't supposed to be much higher than Level 3 or 4 Warriors. This means that a properly equipped Level 20 PC is generally able to wipe out entire metropolises by himself.
Considering that an ordinary citizen has maybe one or two HP, and no attack can do less than one HP... and a housecat got three attacks per round, there was a good chance that a group of strays could take out a town. Lampshaded terrifically in thisOrder of the Stick webcomic.
A warforged (magic robot) crusader could literally do this all day. If the population of a planet of commoners engaged him and he took the cleave feat chain and perhaps had a good movement speed he could seriously keep fighting until they all died. With the right maneuvers and or feats it could do this without equipment.
Eberron went out of its way to emphasise this point, stating that by the time the party reaches 5th level they've already overcome more than your standard city guard will face in a lifetime.
In First and Second Edition it may have been even worse: Non-classed humans (and halflings) were considered less than 1 Hit Die creatures. The warrior classes (Fighter, Paladin, and Ranger) had the "Sweep Attack" that could be used against up to the character's level in foes of less than 1 Hit Die per round. At level 20, that basically meant that the expectation against a mob of level 0 foes would be 19 kills per round (#20 would be the automatic miss on a roll of 1).
Nobilis are certainly capable of embodying this trope, considering the characters are literal gods. One of the higher level miracles (but certainly not out of reach for any Noble) gives the actual example 'fight your way through an army alone, one by one'. However, Nobilis prefer to manipulate things from behind the scenes, and feel that if things give over to full-scale combat, everyone has already lost.
RookCatchfly is a case in point; at Aspect 4, she's spelled out as being strong enough to beat the crap out of the entire United States Marine Corps.
Leaving aside game mechanics, the fluff tends to keep this more-or-less limited to high-level spellcasters, who have a tendency to be able to wipe out entire armies of mooks with a single spell.
Werewolf: The Apocalypse has you playing men and women who can turn into wolves (or sometimes wolves who can turn into men or women) who also sometimes find it expedient to become nine foot tall death-dealing monsters that heal almost all wounds virtually instantly and who can move at absurdly fast speeds. A combat-oriented starting character won't necessarily win a duel with a main battle tank, but it's not an unreasonable outcome.
On the other hand, while starting Vampires were much weaker than starting Werewolves in Vampire: The Masquerade, the most powerful Kindred easily qualified as this. A single werewolf at start of game could take out a small town in a single night. A Methuselah-level vampire with Vicissitude could turn an entire city into living sausage. And even an army of them would get curb stomped by Caine. Luckily, pretty much all the vampires who are that old are hibernating right now.
In Exalted, while any character who's even vaguely combat-focused is likely to be this, high-Essence Solars can learn a charm called In Doubt of Legions Spirit, which lets them fight entire armies single handedly at no disadvantage whatsoever.
Indeed, for Exalted players, the entire trope gets condensed into a single word; Dawn. Dusk would be a close runner up, if they weren't more accurately described by the term 'One Man Apocalypse'.
The Big Boss of the aforementioned Slayers, Malfeas, is an even bigger One-Man Army (emphasis on big). One of his souls, Ligier, counts as an army just by himself, and Malfeas has a lot of souls. Slayers' hell-field pales compared to Ligier, for he is the green sun of Hell. Stat-wise, he can fight the Unconquered Sun by his lonesome, something he's been aching to do for millennia.
In what we've heard of the third edition, the Legion of Silence are hard enough that one Legionnaire versus 100 bandits leads to a Curb-Stomp Battle in which the Legionnaire only suffers a minor wound during the brawl.
In Scion you play as the child of a god, imbued with some of their power. If you focus on things like strength and stamina, it's very likely that you could slaughter scores of normal people single-handed. And by the time you've advanced to demi-god status you officially count as a Person of Mass Destruction.
In Strike Legion, this is the end result of the Star Republic's Legion Process, which turns a small number of suitable candidates into nearly unstoppable Super Soldiers. Aside from grating a dramatically reduced aging process and making the Legionaire virtually immune to disease and poison, it also makes the Legionaire superhumanly fast and stronger, tougher, smarter, and able to break reality. Then the Republic gives the Legionaires access to hyper-advanced weapons and equipment, Powered Armor, battle frames, and a Strike Cruiser, all of which are able to lay waste to entire armies of their counterparts on the Imperial side. This is all so that the Legion can carry out impossible missions that the regular military can't. On the opposite side, the Imperium produces their own One-Man Army troops, some of which can match the Legion in direct combat.
In The Lord of the Rings Strategy Battle Game, a number of heroes - most notably Aragorn and Sauron - are more than capable of cruising through a staggering number of opponents. One memorable battle report in White Dwarf had the entire Good army slain or fleeing except Aragorn, leading to him strolling through the remnants of the Evil force, batting off the troops and shrugging off a direct sorcerous attack from a Ringwraith, and reaching the objective by himself, limiting the Evil side to only a minor victory.
The "Exalted" mechanic in Magic: The Gathering encourages this. Each creature with "Exalted" grants a +1/+1 bonus to an attacking creature if it attacks alone. Buffed by the prayers of others, even a lowly normal human soldier can become strong enough to slay the mightiest monsters.
Mark Harrigan from Arkham Horror has "One Man Army" as his ability. What does it do? He can't be delayed or arrested. Ever. He also has a flamethrower in his starting equipment.