Ezio Auditore in his trilogy is a story how he moves from this trope all the way up to Big Good as well.
Connor in Assassin's Creed III is a tragic desconstruction of this trope: he embarks on his quest to save his tribe and avenge his mother who was killed by a fire started by the Templars, and ends up sympathizing with the Colonists' side in the Revolution. However, it turns out nothing as simple as his world views presumed and as he succeeds in killing all his opponents, he fails to protect his people and ends up having to kill his father Haytham when he tried to murder him. And oh, it was the Colonists who gave the order to attack his tribe and not the Templars, meaning he has been assisting the side that ends up driving them away.
Alexios or Kassandra in Assassin's Creed: Odyssey can be played as straightforward heroes at the player's discretion by assisting others free of charge, be kind as helpful as they can and opposing the Cult of Kosmos.
Yugo from Bloody Roar goes from investigating the mysterious circumstances to his father's death to leading a resistance against a corrupt corporation trying to exploit zoanthropes and aims to make a bright future of co-existence between humans and his people.
Monica from Dark Chronicle, in one of the few cases where the main protagonist is not also the Hero.
Darkstalkers is a bit complicated about it: Demitri Maximoff was supposed to be the actual protagonist of the series, until Morrigan Aensland took over his place, but neither of them fit the traditional heroic archetype since they are morally ambiguous of varying degrees and motivated by power and hedonism, respectively. Donovan Baine is the closest one to qualify due to being motivated to hunt evil monsters and he is the one to confront Pyron in the OVA.
Although there's the possibility of it being too obvious to be worth listing here, the majority of the main characters in every Dragon Quest game serve as the Hero, to the point that in Dragon Quest VIII the hero's default name is Hero. Nearly all of them have balanced abilities and use (or have the option of using) swords, and many of them have lightning and/or fire in their selection of attack magic. One of the only exceptions is the Hero from Dragon Quest II, who learns no magic at all and serves as the physical fighter of the party.
And as if to drive the point home, when the Heroes of Dragon Quest III, Dragon Quest IV, Dragon Quest VIII and Dragon Quest XI came to Super Smash Bros. Ultimate, they all shared a slot under the same name, which is, you guessed it, Hero.
Daggerfall: The Agent, a personal acquaintance of Emperor Uriel Septim VII sent to the eponymous city to investigate the death of its King, who quickly becomes embroiled in a plot to reactivate a Lost Superweapon that will forever shape Tamriel. (Literally, as the case may be.)
The Civil War questline is nearly as expansive as the main quest, and has the Dragonborn work with either the Empire or the Stormcloak rebels as essentially a One-Man Army to claim Skyrim for one side or the other.
Dawnguard follows the Dragonborn who can choose to work with the eponymous Vampire Hunter organization against a powerful group of vampires who seek to invoke a prophesy to bring about The Night That Never Ends, or work against the order as one of the vampires.
Dragonborn has the Dragonborn visit Solstheim, where he/she comes into conflict with Miraak, the first Dragonborn who seeks to return.
In the Fable series, Heroes are a classification of people in Albion who possess the disciplines of Strength, Skill, or Will, and as such have extraordinary fighting and magical abilities. The player character in each game has control over all three disciplines, and can either play this trope straight or horribly invert it.
Played straight in most of Fallout 3, but subverted in four of the five add-ons (Broken Steel being a continuation of the main storyline, very heroic, and something of an Author's Saving Throw for the original ending). The main game revolves around one man's dream to bring free, radiation-free water to the Wasteland, and how his child either achieves or subverts that dream.
Operation Anchorage requires the player to aid one of the least sympathetic non-psychopathic factions in the game (who only exist as a faction because they broke away from a group that decided it was more important to protect innocents from 8-foot-tall genocidal mutants than to hoard technology).
The Pitt forces the player to choose between allowing miserable slavery to continue in the name of rebuilding the only working steel mill on the east coast and finding a cure one of the most devastating mutations in the Wasteland, or freeing the slaves by replacing a Reasonable Authority Figure with his treacherous lieutenant, who then plans to use his former Lord's infant child to find a cure as fast as possible, her health be damned. Also, it is implied that choosing the latter will allow the steel mill to rot, a significant setback for rebuilding.
Point Lookout has the Lone Wanderer caught between a badass and a Chessmaster. While none of his actions are decidedly heroic or villainous, he gets outsmarted by brain-damaged drug addicts and (depending on what side quests he follows), a 200-year-old death trap. Both these events paint the hero as more of a gullible imcompetent than anything else.
Mothership Zeta is mostly a fight for survival, ending with the player willingly destroying a craft capable of traveling to other planets. That, you know, aren't ruined.
Tidus from Final Fantasy X is clearly the main character to the player, but he's a late-comer to the other characters, who already composed the rest of The Team before he showed up.
Yuna takes up this role in the sequel. Very interesting considering that she was The Chick in the previous game. She even fights like Tidus and uses one of his swords in her Warrior dressphere.
There is also a character class called "Hero," but that's a bit of a misnomer as they're simply the promotion of the Mercenary and/or Fighter class.
Glory Of Heracles III plays with this by having two nameless Amnesiac Heroes whom the player names, the first party member and the final party member, with the two referred to as "the Hero" and "the Protagonist." There's a very good reason why the main character isn't "the Hero."
From Halo, Master Chief Petty Officer John-117 of the Spartan-IIs. Not the strongest, fastest, smartest of the Spartans, or the best at any category at all, except in leading the others and always getting the job done. He is so unbelievably Mario in comparison that even though there is at least one Spartan that can do something better than him, he wins everything because there is nothing he is bad at. Nothing. And he knows it. That's why he was made The Leader of the rest. Although Cortana says he has one thing the rest didn't: LUCK.
Another thing he is the best at is being the Bravest with a capital B, as said by Dr. Halsey herself. Spartans are by definition extremely brave and invulnerable (latter mostly as symbolism, but also proven with them having the best survival rate per engagement). However John takes it to the pure insane, combining it with his luck and courage to do the pure impossible even by Spartan standards.
Black Orchid in Killer Instinct is considered the main protagonist of the series due to having appeared in every game and being the canonical victor, though she arguably shares the role with her brother Jago.
In Kingdom Hearts: Birth by Sleep, Aqua is by far the hero. She is the only one to achieve the rank of Keyblade Master, never succumbs to darkness, puts her friends above herself, and always fights to help others above all else.
The Legend of Heroes: Trails in the Sky First Chapter and Second Chapter has Estelle Bright as the main protagonist of the game and the heroine of the story, who starts off her adventures as a bracer.
The Legend of Heroes: Trails in the Sky The Third has Kevin Graham who was a party member in SC and ends up being the hero of his own game as he struggles with his mistakes and failures, and learns to accept them.
Zero no Kiseki and Ao No Kiseki follows Lloyd Bannings who aspires to be a policeman and also wants to know who and why his brother was killed on duty.
Rosalyn from Okage: Shadow King is another case of the hero not being the player character, generally being a superb Hero's Guild Member and overshadowing Ari. But then, everyone does that last bit.
Devlin McCormack from The Orion Conspiracy. Unlike a lot of games out there, he is different. How so? For starters, he is a middle-aged guy who has a number of issues. He was not a good father or a good husband. He does feel bad about it. His son and wife are both dead. He fought as a soldier in the Corporation War. However, the game demonstrates that he seems to prefer using his brains and guile rather than a gun and physical combat. He also engages in lying, petty larceny, blackmail and some Shoot the Dog moments. The Chick is also not attracted to him. With all that said, he does lead the charge more than once in the game.
Prince of Persia: The titular nameless prince in nearly all the games except Prince of Persia: Warrior Within and Prince of Persia (2008) where he is more of an Anti-Hero where he is fighting for his own self-preservation in the former and is a thief and grave robber in the latter. In all other games though, he is more traditionally heroic trying to save the princess from some evil vizier or a terrible sand monster unleashed upon the land.
Quest for Glory: Unsurprisingly, the main protagonist titled as the Hero (though his canon name is Devon Aidendale) is this trope by profession. Though he can pursue any class from Fighter, Mage, Thief and The Paladin, the whole series is about becoming more virtuous and heroic as it progresses.
In Sly Cooper, Sly is the hero even though he's a thief. Even though he's considered a criminal because he steals, he only steals to save the world from criminals who actually are evil and have devious intentions.
Soul Series: Sophitia was canonically the one who defeated Cervantes and destroyed Soul Edge at the end of the first Soul game. Later games would put Sophitia as a supporting character in favour of Xianghua (Calibur), Siegfried (Calibur II, III and IV), Sophitia's sonPatroklos (Calibur V), and now Kilik (Calibur VI). Sophitia however has the most in common with traditional fighting game heroes, being the balanced, newbie-friendly character.
Deconstructed hard in Spec Ops: The Line. Captain Walker's desire to be a hero is what causes him to kill American soldiers, drop white phosphorous on innocent civilians and generally sentence every person in Dubai to certain death.
Guile also fits this trope. He is the one who consistently takes on Shadaloo, and is arguably one of Bison's greatest adversaries.
Rashid from Street Fighter V also qualifies. While Ryu delivers the final blow on Bison, Rashid is ultimately the guy who saves the day by stopping Bison's doomsday machine. Rashid also has more storyline fights than anybody else and he is the character given the most screentime, by far.
From Super Mario Bros., Mario. He names the franchise, is the main playable character, is the Jack-of-All-Stats, etc., etc. Also Luigi, being Mario's brother and sidekick, can be considered to be this.
In the Tekken series, three fighters are suitable to this role:
Jun Kazama is officially this for Tekken 2, beating Devil and all.
Her son, Jin Kazama fulfills this role in Tekken 3 and 5. And judging by his actions at the end of 7, he's set to return to this role when 8 rolls around.
Lars Alexandersson seems to be taking over this role in Tekken 6, what with Jin Kazama going on a rampage.
Vampires Dawn: Valnar is the main protagonist and will fit this trope like a glove if played Friendly Neighborhood Vampire. At least the second game assumes you played it this way, given it starts with one ending where you were a good guy.