Fictional heroes tend to be a diverse bunch, but most have one thing in common: a morally positive motivation. Even morally questionable heroes usually are at least partially motivated by a genuine concern for others, desire for justice, belief in playing by the rules, etc.
The Nominal Hero is the exception to this rule. While at least technically on the side of good, their motivations are neutral at best.
So why are they on the side of good? Usually, it's one of the following:
Annoyance. For these characters, It's Personal. Maybe the villain was rude to them in the past, or maybe they think the villain’s costume is tacky. They aren't interested in fighting evil, they want to see their opponent defeated. Often overlaps with Enemy Mine.
Boredom. These characters are basically fighting for good because they don't have anything better to do. They don't care if the heroes actually succeed, they just enjoy the adventure. A Heroic Comedic Sociopath or The Trickster might have this motivation.
Mutual Interest. These characters have selfish reasons to hope the heroes succeed. Often, they are characters who would normally be villains, but their future plans are threatened by a mutual enemy. Often an Enemy Mine. A Magnificent Bastard might aid heroes to manipulate events in their favor as a standard tactic.
Relationships. Not every Nominal Hero only cares about themselves. Some Nominal Heroes have a love interest or someone else they do care about. A Nominal Hero might do something heroic to impress or rescue that someone, even though they couldn't care less if other people die.
Reward. These characters want something in return for their help, such as a share of the treasure, or simply something to look good on their resume. They aren't interested in whether anyone else benefits. The Miles Gloriosus is an example of a character type that might choose to join a band of heroes for this reason.
Force. Some characters become heroes because they literally aren't allowed to be anything else. Maybe they're on an Explosive Leash or are a Cosmic Plaything, but when they fight for the side of good, it's only because it's their only option other than perhaps death.
This type of hero is rarely averse to working alone, with other heroes, or for the Big Bad, if they think it is in their interest. Being a Heel Face Revolving Door is no big deal, because from their point of view, they never really switched sides, just tactics. When working for a villain, it will usually be as a Dragon with an Agenda, Psycho for Hire, or The Starscream; this character will betray the villain the moment the villain's plans interfere with their own. On a team of otherwise conventional heroes, they'll often be in an Enemy Mine, Sociopathic Hero, or Token Evil Teammate role. Other heroes may only work with them because they could use all the help they can get, or specifically to keep an eye on the hero-in-name-only, so that they don't become a more serious threat.
In terms of sympathy, Most of Nominal hero's examples are Noble Demons.
Many other tropes about questionable heroes can overlap with Nominal Hero, but most are not true subtropes:
In Dragon Ball Z, Vegeta goes through a Nominal Hero phase as part of a several - arc Heel Face Turn, starting in the Namek arc as a Villain Protagonist seeking to overthrow his former master, and in the Cell and Buu arcs, defending earth, but only for his own selfish reasons. After his death and subsequent pseudo-revival in terms of coming back to Earth for one day, he fights for the Earth for the sake of defending it for the first time.
In Death Note, Mello is solely dedicated to being the one to stop Kira and is more than willing to become a mob boss, kidnap innocent girls, and in the manga, even threaten the President to sabotage his rival so said rival can't catch Kira.
Guts of Berserk during his phase as the vengeance-obsessed Black Swordsman was very much this. An utterly ruthless warrior who cared about nothing except killing demons, and would not lift a finger to help innocents caught in the crossfire, considering them small fry without the strength to truly live, and in many cases, he could be seen as even more horrifying than the Apostles that he was driven to kill. Only after finding Casca again has he been able to move out of this territory, though he still has to deal with a particularly nasty Enemy Within that represents who he used to be.
Mugen of Samurai Champloo is a Blood Knight who will frequently abandon his companions in the name of pursuing a good fight, and cares little for his promise to Fuu, instead trying to fulfill his promise to kill his rival, Jin. That said, he goes through a lot of Character Development by the end. Enough so that he honors his companions as true friends.
Jin isn't much of a hero, either: though he operates by a pragmatic code, the first episode establishes him as something of a Reluctant Hero - if he happens to be at the right place at the right time, and something seems to be in it for him, he'll help out. His cold disdain for his companions is apparent, and he stays with Fuu for the same reasons as Mugen: he has nothing better to do and he wants to kill his rival. However, he also undergoes significant character development, explicitly naming Mugen and Fuu as his first true friends by the end.
Kanta has no real redeeming moral qualities and doesn't care about anything except money, boobs and staying alive. However, much of his work ends up being vaguely heroic because of the jobs he's assigned tend to be things like "Take out this gang terrorizing our town." By the end of the series he crosses the Moral Event Horizon and does a Face Heel Turn.
Junko is equally amoral and only not a villain because her job is taking out people who tend to be worse and like Kanta, she ultimately pulls a Face Heel Turn.
Rainspider is a heartless enforcer for loan sharks and implied deviant who has a tendency to abandon his teammates when battles are stacked against them. However, he's hilarious, and always follows his fleeing by a Big Damn Heroes moment at the right time. He's kind of more likable than Kanta, if no morally better.
In the Anime version of Afro Samurai, the title character is something of a tragic example of this; he is not without some humanity in him, but ends up burying it in his all-consuming pursuit of vengeance and adherence to his brutal code of honor, to the point where it's not clear whether he;'s a Nominal Hero or a Villain Protagonist. Afro's goals are, effectively, identical to those that he fights, and a strong argument could be made that the audience only sympathizes with him because we saw his back story, and didn't see theirs.
Gantz features a number of these. Several of the Osaka members are sadists who get off on hurting defenseless aliens who just happen to be their enemies. For the most part they could care less about their own team mates and threaten to kill innocent people who simply irritate them. One is a serial rapist who rapes female aliens before murdering them in order to avoid being imprisoned for rape. They just happen to be fighting for the good of mankind.
Nao Yuuki of Mai Hime strongly believes that the Himes should use their powers for whatever they want, but allies with them to stop the Searrs foundation. And then she is attacked by the other Himes when they think she attacked Yukariko, loses an eye and undergoes a Face Heel Turn.
Masaru "Kodama" Kodaka of Bokurano, is fighting to save the world like everyone else, but not only does he not care about collateral damage, he thinks it's a good thing, since he sees people as divided into those who deserve to survive and those who do not, and thinks that his father (of the former type) would benefit from being able to rebuild.
Genis-Vell, a.k.a. Captain Marvel, during his "space madness" phase. Genis was, at best, a Villain Protagonist with a severely warped sense of justice and rabid sense of entitlement. Rick Jones, to whom Genis was molecularly bonded, constantly opposed him and (rightly) questioned Genis's sanity. On one occasion, Genis bestowed powers upon a serial killer whom his friend Rick Jones had testified against in order to get the killer to stalk both Rick and his wife, Marlo. After putting Rick through absolute hell to the point where death seemed certain, Genis then executes the serial killer and explains to Rick that all of this was to teach Rick that he only lived on Genis's own whims, and that he was never to question him again.
In Sin City, Miho's motives are unknown since she is mute, but she seems to have loyalty almost exclusively to Old Town. She has assisted Dwight in the past only because he once saved her life but that didn't stop her from essentially threatening to kill him if he interfered while she was torturing a corrupt cop in the middle of a street. Otherwise, the best you can say about her is that she doesn't target innocent people.
In The League of Extraordinary Gentlemen, Hyde, Griffin, and Nemo are a pair of serial rapists and murderers, and a psychopathic pirate, respectively, who are offered an official pardon if they'll turn those qualities against the Empire's enemies. In the film version, Griffin is replaced by Loveable Rogue Rodney Skinner, and Hyde and Nemo get a makeover.
In Sam & Max: Freelance Police, Max considers it a compliment to be called a grade-A sociopath, and was even dubbed the most terrifyingly dangerous force in the universe by the villain in Season One of the Telltale games. The only thing that really seems to keep him in line is his less sociopathic partner.
Latias Journey has an in-universe example in the Red Ranger. An amoral and borderline sociopathic "superhero" is designated as heroic by Mr. Ford.
Latias: So you even denigrate your comrades who fight alongside you. You attack a pair of Pokémon who had done nothing to hurt you without provocation or warning, intend to beat me to a pulp to capture me, and are also assisting a madman with his evil plans. You are no hero.
Red Ranger: Hey, as long as the people of Ever Grande City think I am, and I get paid for my work with money and power by Ford, I don't care what you call me!
In Hulk, it's not entirely clear (until possibly the end) if the title character really knows and/or understands what he's doing.
In The Street Fighter, Takuma "Terry" Tsurugi is a brutal and pitiless man. He sells a girl into slavery and kills her brother when they're not able to pay him for services rendered, and he's not above sacrificing innocents that he's not directly helping. He avoids Villain Protagonist territory by fighting against Yakuza, whom he despises, and working to protect the good guys, even though he does so for his own reasons. In the Video Game version, he's portrayed in a somewhat more positive light.
In Braveheart, Steven the Irishman seems to have only joined the Scots because he'll be able to kill Englishmen, not to help the Scots get freedom.
The Expendables as a whole only fought the likes of pirates and dictators because they were paid to do so. They are, to their credit, remarkably easy to talk into doing the right thing even without a paycheck, though.
When ordered to rescue the President of the United States, Snake Plissken would gladly hijack his transportation and fly to Canada, but a bomb planted in his body makes him do otherwise.
Yarol, the Venusian sidekick in C.L. Moore's Northwest Smith stories, is heavily implied to be this. The narration never specifies his enormities, but hints that his angelic beauty belies his absolutely evil nature.
Uhtred Ragnarsson of Bebbanburg, the main protagonist of The Saxon Stories, is this in his halfhearted service of Alfred the Great. Although he would much rather accompany the Danish invaders, certain events forced him to make an oath of service to King Alfred that he refuses to break.
Raistlin Majere is this in the original DragonlanceChronicles triology. Really the only thing keeping him with the Heroes of the Lance is some lingering affection for some of them and the presence of his brother Caramon. Even during Chronicles Raistlin started drifting towards becoming the Token Evil Teammate and the Face Heel Turn was complete by the next triology Legends. Still he did earn his Redemption Equals Death and had a few Pet the Dog moments.
Live Action TV
Tony Soprano from The Sopranos is a con artist, a thug, a womanizer, a thief, a murderer, an extortionist, and an adulterer - and yet somehow it's nearly impossible not to sympathize with him. The only things separating him from a Villain Protagonist are his genuine love for his family, kindness to his friends, and occasional pangs of guilt and moments of vulnerability. Oh, and the fact that his friends (and enemies) are even worse than he is.
The redeeming elements of his character are largely absent by season 6B, and especially by the finale.
The titular character from Dexter is at the far, dark end of this to the point where he could fairly be considered simply a likeable Villain Protagonist, being a Serial Killer who was disciplined at a young age to channel his sociopathy toward killing other evildoers.
In Kamen Rider OOO, Ankh is only helping Eiji against the other Greeed because it's in his own best interests, and has no qualms about who is hurt so long as he gets what he wants. though he gradually transitions into a Knight in Sour Armor by the end.
In the 2010 BBC modernization, Sherlock Holmes describes himself as a "high-functioning sociopath," and cautions Dr. Watson: "Don't make people into heroes, John. Heroes don't exist; and if they did, I wouldn't be one of them." This shows that his motivations are not those of a typical straight hero, and that he's possessed of a very cynical worldview. His motivation is quite explicitly boredom and a need for intellectual stimulation.
In Father Ted, Father Jack Hackett is a violent, selfish, perverted alcoholic and flashbacks suggest he was once a bullying fire and brimstone preacher and a paedophile. The only thing keeping him from being a Villain Protagonist is that his alcoholism usually renders him too docile to harm anyone. And sometimes it does the exact opposite.
His reasons for fighting the Federation also change as time passes: in Season 1 he claims to have nothing to do with Blake's revolution other than living on the same ship, in Season 2 he's playing along because he wants the ship, in Season 3 the Federation is a threat to his freedom and by Season 4 he genuinely hates them, though by this time he's sliding down the sanity slope and it's hard to tell what his true motivations are.
Most of the other "good" main characters — except Blake, Cally, Dayna and perhaps Jenna and Gan — are being dragged along behind Blake's idealism. They fight because there's nowhere for them to run.
Magna-Defender is like this in Power Rangers Lost Galaxy. He may assist the rangers taking down a monster or two and want to take down Scorpious, but he's only does it for the revenge. This definitely becomes clearer when he tries to destroy Terra Venture because it might destroy Scorpious. Although he gets better, near the end.
The Police (and most other public figures) in The Wire. McNulty is perhaps the most obvious example, stirring things up at the start of the show not because he wants justice for the victims, but because he's kind of annoyed with the Barksdales and Stringer Bell for getting away with so much. In Season 2 he stirs things up again mostly because he's bored, although the chance to stick some revenge on the boss who reassigned him plays a role as well.
Voiree Misallo from 8BitGamers. Though firmly on the side of good after a religious experience and a genetic examination revealing her to be born with a semi-sociopathic defect, her motivation mostly has to do with wanting to avoid hell, keep her boyfriend, and remain friends with her True Companions.
In Marathon, not only does Durandal make it quite clear that he is only fighting the Pfhor as a means of escaping the end of the universe, he is the one who brought the Pfhor to Tau Ceti in the original game, an action that resulted in the deaths of nearly everyone in the colony.
In Hexen II, two of the heroes are the Assassin (who wants to prove she can kill the most powerful and best protected being on the planet) and the Necromancer (who has a problem with Eidolon being more feared than him).
In God Of War, Kratos, to the point that, particularly after the first game, many consider him an outright Villain Protagonist, even worse than the people (or gods) he's trying to kill.
In which case the gods themselves become Nominal Hero antagonists. Their motivations for opposing Kratos are purely selfish, and they have little concern or empathy for humanity itself.
In Drakengard, Caim is this in the first game. The only thing that made him "heroic" in the first place was the fact that he was fighting against an evil empire that was even worse. Once they're defeated, he defaults back to RIP AND TEAR.
Zaeed Massani is a ruthless revenge obsessed merc on Commander Shepard's team. During his loyalty mission, he burns an entire refinery to the ground while callously disregarding the innocent lives trapped inside just to get revenge on another merc who screwed him over 20 years prior.
Aria T'Loak is a crimelord who allows slavery, drug running and pretty much anything else as long as it doesn't undermine her power. She is however willing to aid Shepard to some extent, and seems none too fond of Ardat-Yakshi or the Collectors. Probably both for practical reasons and on principle. In Mass Effect 3, she helps you out of self-preservation because, as she puts it, the reapers are a threat to all existence, including hers, so it's "within (her) interests" to help Shepard.
In the first three Fallout games, an evil player character could be seen as this, since you have the freedom to blow of civilian’s heads with absolutely zero provocation, enslave children and nuke cities. However, this is somewhat moderated by the main story pitting you against monsters who want to wipe out the vast majority of the remaining human race. With New Vegas Caesar’s Legion, the player has the option of becoming a full - blown Villain Protagonist, as they bring the region under the grip of a nation endorsing rape, slavery, child molestation and murder for public entertainment.
Demitri Maximoff from Darkstalkers. He only confronts Planet Eater Pyron and Dark Messiah Jedah because they are a threat to his plans in conquering the Makai, and treats everyone who aren't his servants with great disdain.
Augus in Asura's Wrath only joined the Eight Guardian Generals so he could have exciting battles.
4 of all the Seven Deities are implied to be this
In the Metal Gear series, Meryl, Psycho Mantis, and Liquid claim that Solid Snake is a Sociopathic Hero who enjoys combat and killing, with the latter two telling him that he's far worse then they are. However, Psycho Mantis and Liquid are mass murdering psychopaths attempting to 'kill as many people as possible' and bring on a Darwinist 'warrior's paradise' respectively, which makes their attacks on him border on Hypocritical Humor and possibly Unreliable Narrator as well.
Reaver from Fable II and III. He tries to double cross the hero at least twice and only helps the hero because the Big Bad proceeds to double cross him when Reaver tries to turn the hero over to him.
In the first No More Heroes, Travis Touchdown. The only thing that makes him any kind of hero is that the rest of the assassins are sociopaths. Later, his motivation becomes more heroic.
In Kingdom Hearts II, Maleficent, while still not "good" in any sense of the word, is allied with the heroes in a common goal.
Grom Hellscream and Illidan Stormrage of Warcraft: the first is an amoral Blood Knight and the other is a subject obsessed with demonic power.
In the Super Mario Bros. series, Wario is willing to take on Evil Overlords and the like, but only if there's treasure at the end of the road. Otherwise, he couldn't care less.
In Blood, Caleb spends the entirety of both his games killing everything that moves. The only reason he's the good guy is, excluding a few mimes and other innocents, everything that moves is part of the world-spanning Cabal.
In Ace Combat Zero, Cipher on the Mercenary path. As opposed to Soldier, on this path he's willing to take out anything not specifically on his side, be it enemy combatants, disabled enemy units, or even civilians on occasion.
In BlazBlue, Kokonoe has a few soft spots here and there, but REALLY has no problems in nuking a whole city just so she can claim the frag of Terumi's head... never mind thousands and thousands of innocents who will die along the way.
The King of Fighters' main character Iori Yagami (introduced in 1995 as the rival of Kyo Kusanagi) plays this role. A loner and a very angry and consumed character, he lives to see the defeat of Kyo and won't stop until that happens. He does do genuinely heroic things (even teaming up with Kyo when the situation warrants it) but only so that he can resume thirsting for Kyo's blood. He has no friends and has attacked his own team members in the past (be it willingly or unwillingly when his Orochi blood goes out of control).
Star WarsThe Old Republic Lord Scourge a Sith Lord who is a companion to the Jedi Knight class, he sides with the Jedi to stop the Sith Emperor from destroying the entire galaxy. In the back story he was responsible for Revans capture and the Exiles death because he saw that they would fail in defeating the Emperor. By the end of the Jedi Knight storyline, he is credited as a hero of the Republic, which both him and Satele Shan really don't like the idea of.
Marisa Kirisame from Touhou is mostly motivated by the prospect of magical artifacts to loot. Remilia Scarlet is more interested in maintaining her power than actually fixing Gensokyo's problems (and she's not the harmless kind of vampire).
Sacrifice: The player takes the role of Eldred who use to be a tyrant on his own world, then when his own people turn against him he summoned the demon Marduk to defeat them, then Marduk proceeded to destroy everything else. He is really regretful of having to kill a dragon, but is ok with slavery.
The Daemoness in Sacred: Underworld. At the start of the game she gets stabbed in the back by her master, Anducar, and has a prophetic vision that working alongside the other heroes is her best chance of getting revenge.
Several of the protaganists of Baldur's Gate: Dark Alliance2. Vhaidra wants to hone her skills as a monk so she can take bloody revenge against the assassins who murdered her family, and Borador, as a result of a debt owed to the elves, wants to get his hands on as much coin as he can. Dorn is a borderline example, since his motivation comes across as equal parts 'make the realms a better place' and 'earn as much glory for myself and seduce as many women as I can.'
Dark Pit from Kid Icarus Uprising. He isn't to concerned with the war between the gods. He just likes beating up monsters. After the time skip he gets more involved in order to make sure Pit remains alive, since he learns his existence depends on Pits.
Conker. Guy's primary interest is in stumbling home in one piece, and (with some exceptions), he's not doing anything heroic without some serious compensation.
The Sonic the Hedgehog series has E-123 Omega, who only ever does anything either because it involves his goal of getting revenge on Eggman for abandoning him for other robots, or because Shadow and Rouge asked him to help them out.
Rouge the Bat's main motivation in being a government spy is her obsession with the world's most famous jewels, which she expects to be rewarded with.
In Dragon Age: Origins many of the Grey Wardens. The Wardens will take people of any background with sufficient talents at killing darkspawn from warriors to thieves, to mages, even blood mages as long as they're able to survive the joining. The Wardens have broad powers of conscription that are honored by most governing bodies so many Wardens are pressed into service against their will.
Oghren is a warrior who fights because thats what he was trained to do and his training left him going stir crazy in dwarven civilization. He joins you to find his wife and stays with you because it means he can start swinging his axe again. Nothing more.
Morrigan is a witch with a dark background and little to no regard for the well being of others. She's only with you because her mother told her to come and only helps because killing the darkspawn is in her best interest (though she can develop an attachment to the main character depending on how you play.)
Tyler Smith in Clear Vision, whose motive is sole money and later to save his beautiful wife, in every shooting he does regardless if the targets in question are actually evil.
Isaac Clarke, the protagonist of the Dead Space Series. In 1 and 2, he's just an ordinary engineer who wanted to survive the Necromorph Zombie Apocalypse. In the third game, he literally had to be coerced to get back into the fight, and even then only agreed because he learned his ex-Girlfriend was in peril. However, near the end of all three games, he ends up pulling a Heroic Sacrifice, willingly entering a situation that would likely result in death in order to end the greater threat+
Returning to Aegis VII to bring bring the Marker back to its pedestal in 1, assaulting an overrun Earth Gov base to destroy the Golden Marker in 2 (which would cause a station overload), and staying behind to kill a Brethren Moon before it could find and consume the rest of humanity in 3. In all cases, when Isaac made his decision, he was in or right next to an escape shuttle
Garrett of Thief doesn't really give a damn about anyone other than himself. He winds up in the "hero" role primarily out of circumstance: the Big Bad is usually (in addition to their main plan) gunning for him personally for one reason or another. Also, it's of no benefit to him if The City is destroyed, then where would he do his thieving?
Eugene Greenhilt swore a Blood Oath to defeat Xykon the Sorcerer because the latter killed his mentor, but he was the one who muttered "yeah, whatever," afterwards. He was a horrible father, an inattentive husband, and the small amount of interest he has in Xykon being defeated is only because that oath he swore is keeping him from resting. He's only barely inside heaven in the afterlife. When his son Roy died and went to heaven, Roy was able to get much further inside heaven because unlike Eugene, he actually gave a damn and did everything he could to fulfill the family oath.
Belkar Bitterleaf is an unapologetic Heroic Comedic Sociopath with no actual redeeming qualities. At one point, Roy claims that the only reason he keeps Belkar around is to keep him from using his abilities to become a full-blown villain. Belkar's Stupid Evil antics are entirely deliberate on his part, as he finds being his own personal Mook Horror Show is not only entertaining but also an effective way of gaining XP. Later, he shifts to a more subdued Token Evil Teammate role, and gains an actual Morality Pet of sorts, his Right-Hand Cat, Mr. Scruffy.
In Sluggy Freelance, any time Bun-Bun does something good in the series, Pete Abrams is always careful to give him a completely selfish reason (usually either that the good guys bribed him, or that the villain happened to piss him off). It's rare that he's implied to do anything solely because he cares about a member of the main cast.
Captain Hammer of Doctor Horrible's Sing-Along Blog 's only qualification as a hero is that the guy he's fighting is trying to get into a supervillain organization. He may look like The Cape, but underneath his dashing, larger-than-life demeanor is a misogynistic, self-centered, bigoted glory hound who's far more interested in his image than in actually helping people. This makes him the antagonist of the story, set against the nerdy, Technical Pacifist, Shrinking Violetprotagonist, Dr. Horrible.
In Whateley Universe, the Scourge, which in the distant past has destroyed entire galactic civilizations in its efforts to defeat Mythos monsters. Sociopathic Hero Jobe Wilkins may fall in this trope as well.
Spoony (The character, not Noah Antwiller) is a sleazy pervert and a confirmed rapist as both The Nostalgia Critic and The Nostalgia Chick found out the hard way. The Chick herself is a sociopath with no qualms when it comes to tormenting and manipulating her best friend.
Bender is an extremely selfish kleptomaniac, and thus falls into nominal heroism at times. However, much of this can be excused by the fact that as a robot, he does not fully understand human needs and emotions. He also has quite a few Pet the Dog moments.
Zapp Brannigan is a cowardly, vain, selfish, ignorant, womanizing Jerkass whose incompetence is of epic proportions, and whose battle plans often if not usually call for callously sacrificing thousands of lives in order to further his own career. Nonetheless, he is a key asset for DOOP.