These superheroes just aren't called superheroes. They often don't wear costumes or use code names, but they have abilities far beyond those of normal men, and are superheroes in all but name.
Occasionally, such stories will lampshade the trope by having characters in off hand discussions about whether they'd look good in a cape, or using Something Person-style nicknames, but discarding the ideas as being "silly." A "This Is Reality" remark can be thrown in, as well.
Like many tropes this one has underlying practical considerations, such as:
Aesthetics (most classic comic book-style superhero costumes tend to look very silly in live action, which is why Movie Superheroes Wear Black)
Genre Shift, when the creator is actually aiming for the story to look and feel as if it belongs in Science Fiction or Urban Fantasy categories, and does not initially realize that the story fits the conventions of the super hero genre. He/She may or may not act kindly to people pointing out the similarities.
Marketing (Some creators may wish to avoid their characters being seen as superheroes in order to prevent incorrect expectations of the work)
This is actually more averted after the first series, as the interquel manga, set after the Masquerade is exposed, the news does explicitly compare Contractors to comic book characters. Also, as of the second season, Hei's not the only character who wears a costume. A female Contractor with Implausible Fencing Powers dresses in a black "ninja-like" outfit and a guy not only has a magic-themed power and Renumeration, but he also dresses like one as well.
In a flashback to the Heaven's Gate war, Bai is shown to dress similar to a superhero.
Lelouch in Code Geass dresses as Zero in costume, cape, and mask and turns his Large Ham quotient up to 11. He is a definite fit for the Rich Idiot with No Day Job idea. It's definitely implied that Lelouch was inspired by superheroes, as side materials make off-hand references to him liking comic books and Toku as a child.
He promoted himself to Batman as a PR move. He called his terrorist organization 'The Black Knights' and had them publicly running around defeating drug dealers and terrorists with less PR-savvy. (He also actually employs a professional news-spinner to work on his PR in this period.) Though the suit itself is agreed to look more like Space Dracula.
Li'l Slugger from Paranoia Agent: While hitting people in the head with a baseball bat isn't much of a superpower he definitely invokes a secretive vigilante image.
Superheroes tend to invoke silly images instead of creepy. Superheroes, when they have masks, either obscure only part of the face or are form fitting. V is neither. His outfit would be much more suitable to a conventional villain in most comic universes. The world he lives in has heavy censorship laws so it makes sense that many characters would have no idea what a superhero was.
V explains the importance of his face-obscuring mask to Evie just before the end of the story. He wears it because if people knew his face, he would be just a man, but as "V" he is an idea, an icon, a symbol for people to believe in. Also, so that Evie can succeed him without anyone knowing the first V has been killed
V actually wears tights and is one of the completely justified male examples of such hero. His persona is a XVII-century soldier and so his costume is a recreation of the historical garb that included tight-fitting breeches, doublet and a cape. Without the mask, he could quite well fit the crowd on the London street in an Elizabethan era.
Perhaps in an attempt to capture the tone of the X-Men movies, the entire second volume of New Mutants had the kids operating without any costumes. However, once the series was cancelled and relaunched as New X-Men: Academy X, they all started wearing proper superhero uniforms.
Despite Molly Hayes' most enthusiastic efforts, the Runaways do not have costumes (unless you count Xavin's Super-Skrull suit.)
The graphic novel The Avengers: Endless Wartime, has Wolverine operating without any sort of costume, in order to make him more closely resemble his counterpart from the X-Men movies. The other Avengers do wear costumes, since their Marvel NOW! outfits were explicitly designed to make them look more like their MCU counterparts.
In the early issues of Wolverine's first ongoing series from the late 1980's, writer Chris Claremont intended to have the book focus less on superheroics and instead more on adventure stories in the style of old school pulp magazines. To enforce this, Logan didn't appear in costume at all for these initial issues, and he didn't start regularly wearing his costume until #14, which by that point Claremont had left the book.
Scarecrow just wears a business suit and a mask in Batman Begins, rather than his traditional costume from the comics.
Talking of The Dark Knight Saga, the second film opens with a series of fake Batmen, in loosely-fitting suits, and armed with guns, confronting the Scarecrow and the Chechen. Batman confronts and eventually overpowers them all, reprimanding the fake Batmen for getting involved. One of them asks how he's different from them, to which, Batman invokes, or rather, inverts the trope.
Batman: I'm not wearing hockey pads.
The Blade series. In large part because the first film was released at the tail-end of a period characterized by some of the worst superhero movies ever made, meaning that the film had to avoid too many direct connections to superhero movies. Then again, Blade's comic counterpart never wore spandex anyway which might have led to the film studio's being more willing to bring him to the big screen.
Drive: The Driver's satin jacket with its scorpion motif is akin to this. In interviews, Ryan Gosling and director Nicholas Winding Refn have both likened the character to a superhero. The song "A Real Hero" plays over the end credits.
The Green Hornet: Kato explicitly states "no tights" in the 2011 movie. The Green Hornet actually predates the spandex trend in superheroes.
The first half of Hancock features the titular character dressed as an ordinary person, usually the same clothes a homeless bum would wear. The second half had him in a black leather flight suit as part of his efforts to clean up his act. It's more of a modern film superhero outfit than something you'd see in a comic book; he even refers to it as a Wolverine outfit when initially refusing to wear it.
In Kamen Rider The First and Kamen Rider The Next, the Riders wear biker-outfit versions of their iconic suits. The chests resemble body armor, and the colors are toned down. However, said colors are in the same places as on the original suits, and the bug-eyed helmets remain. They look like bikers more than superheroes from The Seventies while still recognizable as Riders 1, 2, and V3.
King of the Rocket Men, a movie protagonist from the late 1940s the Rocketeer was based on. His attire is even more mundane than the Rocketeer's as it consists of regular black flyer jacket and pants (the helmet is pure Narm though).
The characters in Iron Man technically don't wear spandex. Some wear Power Armor. The closest anyone gets to tights is Black Widow, who wears a black catsuit at one point. Additionally, Tony Stark has no Secret Identity and the term Iron Man is essentially just the name of the armor. Everyone else goes by their real names.
Thor plays with this trope. People in Asgard wear battle armor, capes, and other clothes which look close enough to tights. When Thor travels to Earth, however, he is stripped of his armor and wears normal clothes until it's time to go back to Asgard. As such, the costumes don't stand out in more "realistic" looking scenes. When they are shown, it is in the realm of Asgard which fits the fantastic setting and seems perfectly natural. Thor technically does not have a codename, either. Thor is his real name.
Captain America: The First Avenger has Captain America's iconic spandex outfit show up as his USO costume, which is intended to look fairly ridiculous. When he goes into combat, he wears a more standard battle fatigue outfit with a stars-and-stripes theme. However, when Cap next appears in The Avengers, he's wearing an updated costume heavily based on the USO mascot outfit. Said outfit is explicitly stated to be tights.
Captain America also plays with the trope concerning Bucky. He doesn't wear tights, but Bucky in the comics didn't wear tights at all, but a blue miliary uniform that sorta looks like tights. Bucky wears a suit very similar to what he wore in the comics, only without the Domino Mask. It also looks slightly less silly as, unlike the comic, Bucky is a fully grown man, possibly older than Steve, while in the comics, he was a kid still in his teens.
In the comics, the men and women of HYDRA generally wear green and yellow costumes with masks. In The First Avenger, they're all clad in black body armor and helmets.
Montgomery Falsworth is a costumed superhero named Union Jack in the comics, but appears as a member of the Howling Commandos in the film. As such, he has no costume to speak of.
The Punisher's titular protagonist has an outfit which has always been function over form (the big skull baits Mooks to shoot at his armored chest, he wears holsters and ammo pouches all over), but his first movie didn't even give him his iconic logo. The second and third film versions slap the skull front and center on his chest, however.
The Terminator sequels (including The Sarah Connor Chronicles) fall into this, though admittedly the non-powered, human protagonists tend to get at least as much screentime as the butt-kicking cyborgs sent back in time to protect them.
The X-Men films have generally steered away from wearing the comic book outfits.
Lampshaded and semi-straight in the first X-Men movie, which has the characters wearing dark-color body armor-suits. Wolverine (newly recruited) comments on the outlandishness of the outfits, to which Cyclops jokingly asks, "Would you prefer yellow spandex?" In reference to the early uniforms of the X-Men comic book (and main color of most of Wolverine's comic book outfits.)
X-Men: First Class makes them look more superhero-ish, though. It's not skintight but it is more brightly colored, and ends with Magneto donning something that's somewhere between his classic outfit and his look in the main trilogy.
The Wolverine plays this straight once again, though the Silver Samurai wears a suit of Powered Armor resembling his comic book costume.
According to Kevin Smith, when writing Superman Lives one of the requests from producer Jon Peters was that Superman should not wear his iconic costume, stating that it was "too faggy."
The director of the 2014 Lupin III Live-Action movie has said that Goemon will not wear his iconic outfit from the original manga and TV shows, since in his opinion, a man running around in samurai garb in the modern day would push the audience's Willing Suspension of Disbelief too far.
The Seekers of Truth follow this convention, partly to avoid ghettoizing the story, and partly . . . well, because it's not easy to find a spandex tailor that won't talk.
The Stationery Voyagers only look like they're wearing something along the lines of "tights" to Mantithians. To everyone else, their suits appear to be just spy-geared forms of regular civilian clothing. Then again, how else do you dress six-foot-tall talking Up-Pens, but...like...large pens?
The Animorphs do wear tights, but for practical reasons (see the entry on Magic Pants). Genre Savvy Marco often compares the Animorphs to superheroes, and talks about the idea of making their spandex outfits into actual costumes rather than a random collection of bike shorts and leotards. But it's obvious to all that the Animorphs are outside the category of superheroes in a strict sense, and they fall much more squarely within the tradition of Wake Up, Go to School, Save the World heroes.
The freaks of Those Who Walk in Darkness and What Fire Cannot Burn by John Ridley are just folks — who happen to have one superpower or the other.
For the most part, Aces don't wear spandex, and while many of them have nicknames, these aren't really used to hide their identities.
Remo Williams, the Destroyer:Williams does not use firearms, has various paranormal abilities, has recurring foes, said foes often having special powers, encounters the paranormal regularly. This placing Williams closer to the genre.
The Dresden Files wouldn't look too out of place in urban fantasy series like Doctor Strange and has many concepts that could pass in a superhero setting, except operating in costume.
Live Action TV
Smallville: "No tights, no flights." Clark ends up flying a few times anyway, and then Green Arrow shows up in full four-color superhero getup...
When Aquaman shows up wearing bright green board shorts and a bright orange tank top, Lois says that he looks like Flipper threw up on him.
The show explains it, correctly if not perfectly truthfully, as being the University of Miami school colors.
A small lampshading moment when Chloe walks into a meeting of the Society and the League and asks if this is "costumes only" (Clark wasn't in costume, though).
In Checkmate, Oliver actually denies that his costume is "tights" twice.
This resolution has become increasingly silly as time goes on, because now everyone except Clark runs around wearing a costume. The Justice League and the Justice Society both exist, Doomsday has shown up, and they have Hawkman! Hawkman, with the helmet, and the wings. Apart from Batman and Wonder Woman it's the full DC universe, yet somehow the show insists on keeping him out of his standard outfit.
Until the series finale, and it was more hinted at than obviously shown. Since it was supposed to be the payoff of a 10 freakin' year journey, it certainly could have been done more effectively.
In Lois and Clark, though Supes wears a shiny suit, he's the only one who does. Almost all the villains wear plain clothes and operate in a Heroes-ish 'real-world' manner. For example, instead of wearing a giant light bulb on his head and making dramatic crimes, Dr. Light was an optometrist and blinded Superman by using a ray of concentrated UV radiation to give Superman super-cataracts. (You laugh, but he managed to inconvenience Supes way more than most villains.) The Prankster, instead of being the poor man's Joker, is a Magnificent Bastard who went to the Die Hard school of villainy, his 'pranks' being the crimes that are a misdirection, his real purpose different (and pragmatic and down to Earth) and carried out efficiently. The Toyman was a toymaker fired from a toy company and put mind-altering gas in toys that spread around the city via... the toy store. Oh, and he's also Sherman Hemsley.
The live-action version of The Flash put the protagonist in costume, though they went to great lengths to rationalize it by having his powers shred normal clothing. Only one of his Rogues' Gallery wore anything resembling the gaudy apparel of his comic-book counterpart, though — and that one was a Cloudcuckoolander.
Future!Hiro is kind of wearing tights, but it's more of a ninja thing than a superhero thing.
The only real superhero to appear, St Joan aka Monica was put on a bus before the arc could be completed and shown only in the more outlandish graphic novels.
Buffy the Vampire Slayer — she's referred to as a "superhero" a few times, usually not too seriously. Unsurprising, however, as Buffy takes most of its inspiration, according to Joss Whedon, from X-Men.
Angel — Referenced a few times, most notably by Cordelia when she tries to drum up business for Angel Investigations:
Cordelia: He's already a genuine hero. Would it kill him to put on some tights and a cape and garner us a little free publicity? Doyle: I don't see Angel puttin' on tights... Oh, now I do and it's really disturbin'.
Charmed. There's even an episode where magic turns them into the tights-wearing, Stock Superpowers kind of superhero, called "Witches in Tights".
In many ways, The Doctor: You mean his possessing two hearts, superhuman intelligence, the ability to regenerate his entire physical being and numerous other far-out abilities demonstrated throughout the series aren't superpowers? The main character even has a code name that he goes by in lieu of a 'proper' name.
And the Third Doctor often wore a cape. Granted, he wore it with a velvet suit, a ruffled shirt and a bow tie instead of tights, but the point remains. And in any case, when it comes to the Doctor and the correlation between unusual clothing choices and being a superhero, are we really going to be pedantic, here?
The Middleman comes as close to being a superhero as possible without being openly labeled as one. He even has a super hero name, but no tights. The first episode has him explain his job to Wendy in terms of it being "exactly like your comic books."
Averted by the Power Rangers (and their Japanese Super Sentai equivalents), who are one of the rare few successful live action series where the characters do fight crime using tights and code names.
Worth mentioning, Tokumei Sentai Go Busters is the first Sentai series to ditch the spandex in favor of leather bodysuits. When this information first hit the Internet, it was revealed that Saban (the company behind Power Rangers) had been leaning on Toei (makers of Super Sentai) to make this change for years since they felt that the spandex suits made the shows look too "kiddy".
Sanctuary doesn't do much fighting, but the characters do a lot of using powers beyond things normal people can do. Occasionally played with in that sometimes the abnormals 'save the world' by using their powers and/or putting on actual tights.
No Ordinary Family joins the list. Despite all their talk about super heroes Jim, George, Stephanie, and Katie never even consider Jim or Stephanie wearing masks.
Averted with glorious pride on The Cape. The show is a Reconstruction of Superhero Tropes, and everyone has a code name and at least something gimicky about their appearance. While not tights in the traditional sense, they are more traditional than predecessor series Heroes by sheer fact that they dress up their villains and hero in some way.
Altering one's density would, in fact, be considered a super power. Ergo, he used an artifact which gave him super powers, which still makes him a superhero, in the vein of other superheroes who use some sort of object or artifact to give them super powers (eg, Green Lantern).
Mage: The Ascension, from the Old World of Darkness was periodically sneered at as "supers without the tights". (Mages being mages, they might as well.) A common derogatory term for how some players played sister-series Vampire: The Masquerade was "capes with fangs". In fact all of White Wolf's games essentially feature superheroes without tights — individuals with powers far beyond the ken of mortal men who fight a greater evil. Frequently they even have code names. White Wolf however always tries to paint themselves as far away from superheroes as they think they can get away with; even their most blatantly superheroic game Aberrant features articles about how super powered humans who wear capes and masks and go by code names are not in any way related to superheroes. Werewolf: the Apocalypse was a notable exception, in that one of the suggested Second Edition play styles was actually called "Superheroes," and explains in some details how ridiculously easy it is to fit the Garou into a (dark) superhero-style setting. This was before the Dark Knight, Watchmen, et. al.
The fangame Genius The Transgression doesn't bother with distancing itself from superheroics; in fact it talks about superhero games under the storyteller advice section and has a Fellowship just for superheroes. Still no tights though, just lots of Powered Armour.
This was a result of some players' playstyles, but was not what the writers intended. The word superhero implies a certain constellation of tropes, tone, and ideas which the default tone of each game really didn't fit well, with the possible exception of Hunter: The Reckoning as a deconstruction. Vampire was intended to be gothic horror, Werewolf cosmic horror, Changeling post-modern chivalric romance and Urban Fantasy, and so on. "Individuals with powers far beyond the ken of mortal men who fight a greater evil" would be an apt description of everything from Dungeons & Dragons to Call of Cthulhu (as players learn spells) to Shadowrun, and few would consider any of these games to fit the superhero genre.
Cole, from inFAMOUS, just runs around in perfectly ordinary clothes. He doesn't even bother to hide his face. Doesn't help his face appeared everywhere around the city with claims that he was a terrorist.
A lot of the characters of Metal Gear, and almost all of the vilains could be seen as superheroes. Some have mastered the arts of manipulation and use a huge array of gadgets like Batman, while others have psychic powers that would make them fit in perfectly with the X-Men.
MMO example: City of Heroes's costume generator, despite being based primarily on comic-book superhero stories, allows players to use this trope. Possible costumes can range from the most eye-watering spandex imaginable to normal civilian clothes, and in between.
A few in-game characters have costumes like this, in particular the Dark Watcher.
Deus Ex, where you play as a crimefighter enhanced with nanomachines, which are magic powers and stat boosts.
Tights don't go well with longcoats that play the same role in spy genre as tights play in the superhero genre.
Although Jackie Estacado sports a suit of armor that evokes typical superhero apparel in the the original comics, in the video game edition of The Darkness, he contents himself with just his long hair and coat.
Same New Woman Marita, although she has a hyper-muscular body and extraordinary strength, tries to go on with her old life dressed in plain, normal clothes that cover her up whenever possible.
Many of the heroes and villains from Union of Heroes wear civilian clothes. Probably for budget reasons, because this is a Photo Comic.
Stone, from the same setting, is a Flying Brick whose costume wouldn't look out of place in a biker bar.
The Reliquary campaign featured street-level mystic-oriented superheroes who didn't wear costumes, didn't use code names, and didn't generally get into big, street-smashing brawls. But they were superheroes nonetheless.
The majority of the cast from Phaeton fits this trope, so far.
While most parahumans in Worm wear costumes, there are a number of exceptions, most notably Jack Slash, the closest thing the series has to a Big Bad, who wears a dress shirt and jeans. And then there are a few heroes and villains, such as Narwhal and Siberian, who don't wear anything at all.
Ben 10 (trades in tights for bizarre alien forms instead). He even calls himself a superhero, and each of his forms has a codename. Ben 10: Alien Force put it further by making "Ben 10" an actual nickname.