In an interesting turn of events Mr. Legend turns up to be a Subversion of this trope.
Comic Books
Superman is usually considered the most famous modern example of a Cape. He could just about be considered the Trope Namer; the fact that he wears a cape is one of the main reasons why capes are associated with costumed superheroes.
In the Novelization of Kingdom Come, Wonder Woman probes him for being so visible. He could have easily did all of his superheroing anonymously instead of "showing off like Apollo". Superman replied that he felt that "an ounce of prevention" would do more good preventing crime. She counters that that was the source of all of the other metahuman's desire to do good - through his example.
Oddly enough, the classic Cape on Justice League Unlimited isn't Superman, but golden-age boy scout Captain Marvel. The series also frequently has subplots involving Superman's motivations and temptations despite being The Cape everyone looks up to.
Silver AgeFlash Barry Allen. A CSI with Super Speed powers. Trained police officer, founding member of the Justice League of America. They originally killed him because they couldn't deal with his awesomeness. And then they brought him back to face Darkseid because they couldn't think of anyone else capable of taking him down.
Batman holds himself to enough standards that he is often closer to this than an Anti-Hero, just more on the pragmatic side. But regardless, there's a reason his comics are the Trope Namer for Joker Immunity.
When Superman was dead, Steel took up the role of The Cape and fought "to keep the spirit of Superman alive." Many readers thought he was an even better Cape than the Man himself.
Captain America is probably Marvel's best capeless Cape. As a youth, he tried out for World War II, but was rejected on physical grounds, so he volunteered to be a guinea pig in a military experiment. He did not know there had already been successful trials, and the risk was much less than is commonly advertised; the experiment turned him into a soldier with physical and mental capabilities very slightly above peak human. In the modern era (how he survived is another story), he is such a tactical and moral exemplar that while powerless and wielding nothing more than an indestructible shield that doesn't obey the laws of physics, he leads a team of consisting of powerhouses like Thor, Iron Man, Wonder Man, Ms. Marvel, and the rest of "Earth's Mightiest Heroes". And, despite the name, he figured out he could go against the government and still stand up for America's ideals... and he was killed as an Anvilicious way to "punctuate" the civil war's Family Unfriendly Aesop.
And on a different note, as a young artist he liked to sketch a muscular costumed man called "American Eagle". Later, once it turned out that he would be the only Super Soldier, his remaining experimenters stole the sketches and made a costume based on them. It did not include a cape, unlike the sketch, despite Steve writing "Has to be a cape. So boss!". Much later in the Seventies, when Steve despairs at the corruption of his country, he takes a new identity and sews a new costume, this one caped. Promptly he tripped on that cape, tore it off, and it was never seen again.
Todd McFarlane's Spawn subverts the cape image with minor characters repeatedly pointing out how "faggy" Spawn's superhero outfit looks. Also, he's very much a Nineties Anti-Hero.
Captain Metropolis in the backstory of Watchmen is the closest to emulating the mold... but of course, this is Watchmen. He's noted to have been racist, and was in a homosexual relationship with Hooded Justice. Among the main characters, Ozymandias is a deconstruction of the Cape.
The Comedian is a very brutal deconstruction of the Cape,
Both Nite Owls would also qualify. The first Nite Owl is actually closest to being a conventional superhero out of the whole group.
In Irredeemable, the Plutonian was seen as one of these until his Face Heel Turn. The comic book series is essentially exploring what would happen both is Superman went bad and, by extension, what would happen if someone who ultimately didn't have the moral fibre to be The Cape was given this role.
Bright, Cheery, Mentally-Sound Man from Dark, Brooding, Mentally-Disturbed Man. An "evil" counterpart to DBMD Man (even though they're both vaguely good-ish), BCMS Man is trusting and gentle to a fault. In that he believes violence is not the answer when dealing with armed lunatics and gives mad scientists a stern talking to before escorting them back to their hidden volcano bases to think about what they've done.
The eponymous Empowered might well qualify. For all her faults and frailties, she knows what's right, and will go to tremendous lengths to do just that. In the last story in issue 5, she's willing to very probably die to save Mindf*** , and she only slightly knows the other woman.
In Johnny SaturnJohnny Saturn I is a cape, due primarily to his reputation for integrity and his unwillingness to compromise. The Utopian, especially later in the series, is a cape, and his father Elect is the archetypical cape.
The title of Thom Zahler's independent comic-book sitcom Love and Capes says it all. Issue 10 reveal some practical reasons for superheroes to wear capes.
Thundermind of DC's Great Ten fulfills this archetype despite lacking a cape. As a result, he's the only member of the Great Ten deemed capable of being a media darling.
Cyclops in X-Men, though Depending on the Writer. Some play up his 'boy scout' image, others play up his 'emotionally conflicted and badass leader' image, so he varies on either a cape in charge of the group, or a somehwat reckless, Crazy PraparedFour Star Bad Ass that often makes him look like a Jerk Ass. In general, the most consistent thing about Cyclops is that he is a skilled field leader that lacks the natural charisma of a true "Cape".
All Fall Down has the superhero veteran, Paradigm. Of all the victims of the Fall, he handles it best.
Literature
Captain Carrot of the Ankh-Morpork City Watch, from Terry Pratchett's Discworld series. He has no overtly superhuman abilities, but he combines a strong sense of justice with a fountain of charisma — he assumes that everyone else is basically a decent person, and somehow, they can't help but live up to his expectations.
Of course Carrot is only defined as not overtly superhuman by fantasy standards; he still has a punch that trolls respect and his sword, while "quite the most unmagical sword" most people have ever seen, can stab several inches into a stone pillar. Through someone else. He was raised by dwarfs, who are tougher than humans and stronger pound for pound, and had to get stronger to keep up.
Tycho Celchu. He's a brilliant pilot but not superhuman. What makes him a Cape - well, there's an exchange in Wedge's Gamble that illustrates it.
Horn: "So, you don't even know, really, if you are an Imperial agent waiting to happen or not?"
Celchu: "I know I'm not. Being able to prove it is something else again."
Horn: "But being constantly under suspicion, that's got to wear on you. Why put up with it? How can you put up with it?"
Celchu: "I put up with it because I must. Enduring it is the only way I can be allowed to fight back against the Empire. If I were to walk away from the Rebellion, if I were to sit the war out, I would have surrendered to the fear of what Ysanne Isard might, might, have done to me. Without firing a shot she would have made me as dead as Alderaan, and I won't allow that. There's nothing in what I have to live with on a daily basis that isn't a thousand times easier than what I survived at the hands of the Empire. Until the Empire is dead, I can never truly be free because I'll always be under suspicion. Living with minor restrictions now means someday no one has to fear me."
Wedge, his CO, probably qualifies too. One example: during the Borleias evacuation, the shuttle he's supposed to ride out is destroyed, so he grabs a damaged X-Wing from the vehicle bay. A freighter warns him of nearby Vong ground troops, so he goes and destroys them. Then, while escorting the transport up, they're jumped by a squadron (12, for those of you keeping score at home) of Vong fighters. Wedge proceeds to pull them off the freighter and annihilate the squad, losing his shields in the process. Another squadron catches up to the freighter in this time, and Wedge pulls them away too, despite knowing that there's no possible way he can win. ..except the Rogues showing up.
Gavin Darklighter: "Blackmoon Eleven, what did you think you were doing going after an entire squadron?"
Wedge: "My job."
Subverted viciously in Minister Faust's Journal of Dr. Brain. Omnipotent Man is a semi literate idiot, The Flying Squirrel is a racist, Iron Maiden is a self-loathing depressive etc.
Played straight in the Nightside novels with Julian Advent, who could've been another Dr. Jekyll, but chose to drink a formula that brought his Good side to the fore instead.
In Aaron Allston's Galatea In 2 D, Captain Steele, a full blown superhro. Roger drew him in order to have a really powerful ally but discovered it took too much to get him out of the painting. Uses him in the end, though whereupon Kevin kills him with an Evil Weapon. Roger reveals that he didn't bring him out, he brought Kevin into his painting.
Gently subverted in Wearing The Cape. The more powerful and photogenic superheroes are major media celebrities, who often publicly play to the Golden Age Hero stereotype and have whole marketing campaigns and PR departments to back them up.
Live Action TV
Benton Fraser of Due South, a Mountie who came to Chicago on the trail of the killers of his father, exemplifies this trope, being genuinely polite, noble, selfless and heroic to everyone he meets. In something of a subversion, everyone consequently assumes he's unhinged.
For bonus points, a new genre television show: The Cape. Ironically the title character is actually The Cowl.
Hercules, as portrayed by Kevin Sorbo. He doesn't have a cape or secret identity, but in all other aspects he pretty much fits the bill.
The Crash Test Dummies song "Superman's Song" is actually a fairly interesting, in that it contrasts Superman with Tarzan, to explore the concept of The Cape, as sort of a Reconstruction of the concept before Deconstruction of it became popular.
Optimus Prime, from any incarnation of the Transformers franchise, is a non-superhero example, somewhat like Carrot above but played a great deal straighter. To be fair, Optimus and the rest of his race do fall under the Super Robot Genre category, so to us Puny Earthlings, he seems pretty strong... But his respect for sentient life, his inspiring oratory, his dedication to justice, his courage in the face of impossible odds, as well as being one of the finest warriors and most well-constructed Transformers in history... He's a shining example of this trope, and a beacon of light in a war without end.
A much less publicized character called Countdown is, if possible, even more so. He's no more powerful than Optimus (though his recent Ultra-class figure gives ridiculous statistics for him), but in attitude, morality, determination, intelligence, and so on, he's sort of a cross between Captain Picard, Superman, Thor (from Stargate SG-1), and Carl Sagan.
Video Games
The central figure of the "mythology" behind City of Heroes, Statesman, is a classic Cape. Strict moral code, no-kills rule, monochrome vision, enforces his code upon others and backs it up with literally demigod-like powers. Naturally, he comes complete with an Evil Counterpart, Lord Recluse.
Of course, there is the pervasive theory amongst the heroes (players) of Paragon City that Statesman has a stick magically implanted up his posterior as well.
Then again, he is the current incarnation/holder of the power of Zeus, who was not the warmest or most forgiving of deities.
He is also canonically over 100 years old and has been in the superhero business since the 1920s. So being a little jaded and tired of it all is somewhat understandable.
Ky Kiske from the Guilty Gear series exemplifies this, minus the actual cape. Always standing up for peace and justice, his flaw is his primarily black-and-white view that leads him to be at odds with the lawless-yet-positive Sol Badguy.
Haran Banjo and Rom Stol get turned into these in Super Robot Wars. When all seems lost, Haran Banjo will arrive on the scene (sometimes with a distinct yell of "DAIITAAAARN...COME HERE!!!") and will deliver his Bad Ass Creed and Boast of how Daitarn 3 is here to smash evil ambitions (along with fixing whatever the problem was). Rom Stol one ups this by always interrupting the villain with a yell of "MATE!" (HALT!) before going into a speech about justice, love, punishment et al., sometimes in improbable places (like on top of the stage boss' cockpit). Inevitably, he will be asked who he is, whereupon he declares that they "do not deserve to know [his] name."
From the Global Guardians PBEM Universe, there's Ultra-Man, The Golden Marvel, Centennial, Empyrion, Thunder, Champion, Dharma, Kismet, Shaktimaan, Scanner, Protonik, Paladin, and El Grifo Rojo, just to name a few. Somewhat subverted by The Aryan (a white supremacist NPC crimefighter who most of the players hated to deal with).
The titular villainess of Interviewing Leather has nothing but respect for the "old school" superheroes.
The <3-Verse has Mr Perfect of the Brat Pack as a Cape-in-Training, as well as Thunderbolt and Uncle Sam as full-fledged Capes.
In the Whateley Universe, there are plenty. The Headmistress of Whateley Academy is a retired Superhero and very much fits the The Cape trope, even if her current superheroine garb is a body suit without cape. Since she's been fighting villains since 1943, she has a 1940's sensibility about superheroing... along with over sixty years of experience. She still looks early- to mid-thirties.
And don't forget the 'Future Superheroes of America', better known around the school as... The Cape Squad.
Funny Animal example: Gizmoduck, from DuckTales and Darkwing Duck, derives his super powers from a specially crafted Plot Technology set of Powered Armor, and does not have an Evil Counterpart, but he is The Cape in every other sense of the trope. Charisma, sterling reputation, unwavering principles, black and white outlook on morality, motivated by his sense of civic duty, and flat out the single most personally powerful character in his setting. He also exhibits instances of By the Power of Grayskull! (or as he puts it, "Blathering blatherskite!") and even in-show Lampshade Hanging of The Merch, cheerfully appearing at public events not only to hobnob with his fans and reinforce his reputation as a friend of the public, but also to provide an official market supply for his ever-full fanclub's desire for Gizmo-tchotchkes. In DuckTales, this is not as strong, as the show gave more screentime to his Secret Identity, but in Darkwing, he's almost never out of costume.
Spoofed in Ben 10 with a group of alien superheroes led by a rules-spouting Superman expy. When they 'port in, the current Monster of the Week is less than happy to see them:
Vulkanus: Rrrgh! Capes! I hate capes!
Hego from Kim Possible is a parody of this archtype.
Played with in Megamind. Metroman is a classic Superman Expy Cape (right down to his backstory originating on a doomed homeworld) who grows tired of having to live up to his responsibilities and fakes his death to retire. Megamind is his evil counterpart, who fell into supervillainy after his childhood attempts at doing good went wrong (ironically, at times because of Metroman's competition). After Metroman fakes his death, Megamind then tries to create his own Cape to fight in the form of Titan, which goes horribly wrong (forcing Megamind to finally become the Cape himself to stop him and save Metro City).