Starfox from Marvel comics was not very forthcoming about the psychic part of his powers when he joined the Avengers. He seemed just like a flying brick type to most, albeit a charming one.
I think Batman actually fits into this category very nicely.
Most of the world thinks that he is simply a great detective, athletic and very resourceful.
The fact of the matter is that Bruce Wayne, indeed, has a super-power – the ability to learn very quickly.
Let’s face it – Bruce Wayne is an Olympic level athlete, right? Well, Olympic level athletes spend a lot of time training – every day, for years. And when they reach that level, they still have to spend inordinate amounts of time to maintain their peak performance level.
Likewise, to become a world class detective requires lots of study of police work, forensics and God knows what else. I’m sure it’s not the type of thing to can cover in a Learning Annex class or two – it requires lots and lots of study. And then, again, to stay current, there is constant reading and learning to do on new methods of crime-fighting, etc.
Oh, yeah, and let’s not forget that Bruce is also an engineering prodigy. He probably built (or modified) the Batmobile to his particular specifications. Ditto for any other motorcycles, helicopters or whatever other vehicles he uses. I’d also bet he maintains the labratory equipment in the Batcave (oh, yeah, he’s also extremely well versed in chemistry, physics and biology, no doubt). Knowing how to build and/or maintain all that stuff must take time too.
In short, Bruce Wayne seems to be able to learn all of this in a short amount of time, whereas other people would need years and years (and many more hours in the day) to do so. The easiest answer that I can think of is that Bruce learns things impossibly fast. That is a superpower which he keeps secret from everyone (and maybe doesn’t even realize that he, himself, has).
Zev Steinhardt
You didn’t mention the best bit. He takes on a sidekick and later saves the world in a heroic sacrifice in which the fact that he’s a vampire is revealed. The sidekick then assumes his identity and actually a becomes well-trained ninja who uses special effects to pretend to be a vampire, so the criminals start bringing along anti-vampire gear which of course is useless.
This is a thing of beauty. 
Yes, Coil. And his powers are very similar to those described in the OP. Not the same, no, but just a somewhat more limited version. Which he keeps secret from everyone.
I call this “super-competency”, and the Genesis miniseries seemed to imply that most or all of the “suits” who don’t have explicit powers have this, although not everyone accepts that as canon.
In the Marvel Series Dark Avengers the “Sentry” Character has numerous powers and during his complicated existence was regarded as the most powerful hero on earth. Supposedly his powers came from an enhanced version of Captain America’s Super Soldier serum he drank, but in one story arc it’s more or less stated that, like the Molecule Man, he is basically a sentient cosmic cube.
I should be more clear here. The “secret” is basically that he is not really a super hero with “super powers” he’s (like the Molecule Man) an effectively omnipotent conduit for energy from the Beyonder dimension. The powers he manifests are simply the powers he wants to manifest.
The recent PETER CANNON: THUNDERBOLT series was built around this; he’s basically a honed-his-mind-and-body-to-perfection hero of the mystic kung-fu variety, but can with intense concentration yada yada yada psychic manifestation yada yada yada mighty dragon yada yada yada immune to conventional weapons and et cetera.
So as long as he sticks to his lunch-bucket abilities, he’s a street-level crimefighter. And as for his big-gun power, he’d like to keep it secret – figuring he does more good as the celebrated mystery man who somehow defeated the menacing dragon than as the guy who scared everyone with it and then just, y’know, stopped making it.
So he shills his philosophy with the zeal of a self-help author, is hailed as the world’s leading expert on how nations can stave off further supernatural attacks, and does his best to stop crooks without playing the hoax-exposing ace up his sleeve…
Y’know, when Clark Kent shows up asking questions and someone eventually pulls a gun on our hero before handcuffing him to a radiator in the basement and locking the door or whatever, the bad guy of course later gets his comeuppance from a strange caped alien floating maybe ten inches off the ground with eerily glowing eyes.
But when that happens to Steve Austin, he doesn’t put on a pair of tights or even take off a pair of glasses; from the perspective of the crooks, he just sort of shows back up with no explanation – still looking the same and oh, dang, the dude who’s built like a free safety just hit me pretty hard and now I’m losing consciousness.
When the Man Of Steel is in costume, he meets members of the general public who know all about telescopic vision and superstrength. When the Six Million Dollar Man is in costume – um, no; he doesn’t really have a costume, or a superhero persona; he has some wide-lapel suits and a Kentucky accent.
Despite having a basic suite of superpowers and a superhero-esque Origin Story, Steve generally seems to operate under a different set of tropes: the “secret agent” set.
Superheroes who use secret identities are required to make token efforts to maintain the secret–wearing costumes (face-obscuring or not), avoiding overt use of their powers when in civvies, employing occasional body doubles, and so forth. In return for these efforts, however implausible, their secret is effectively impenetrable except when opposed by a character whose schtick is penetrating secrets–in which case, the exposure must become mutual as soon as possible to maintain balance. Hence Batman can learn Superman’s secret identity via his detective schtick, but doing so requires that Supes actually use his x-ray vision to even things up.
Secret agents, on the other hand, do not generally need to make even a token effort to remain secret. They just are secret; it says so right on the label. They can use the same name on every mission, dress the same, display the same mannerisms and habits, and even be famous. Their antagonists are required to ignore this, because if they didn’t, the agent would no longer be secret, triggering a dangerous genre-quake that could destroy their world, or leave them facing a superhero instead, or…something bad, anyway. The exception is high-ranking members of large antagonistic organization; they are permitted to know that the agent is an agent, in order to demonstrate how powerful and well-informed their organization is. They are not, however, allowed to take the agent’s abilities and resources into account in their plans. This sometimes makes them look like arrogant idiots, but it’s not really their fault. It’s just the way the rules work.
So, when Steve gets chained to the wall in a basement, it’s accepted that he’s going to show up again later. He happened to use super strength to break free, but that’s fairly irrelevant: escaping and showing up in the nick of time is just something secret agents do. If it weren’t a bionic arm, it would be a laser watch, or a vial of acid, or even a hidden lockpick (How unreasonably reasonable would that be?).
The only way the secret agent tropes can work in a series is for the agent to consistently face new opponents or for any recurring antagonists to be part of a Xanatos Gambit. [It’s a trope! </Ackbar>]
[QUOTE=Balance]
The only way the secret agent tropes can work in a series is for the agent to consistently face new opponents or for any recurring antagonists to be part of a Xanatos Gambit. [It’s a trope! </Ackbar>]
[/QUOTE]
I wouldn’t have argued the point – but if you’re going to link to TV Tropes, I’m going to note that they class the Six Million Dollar Man as a superhero.
While that is true, they also explicitly note that it is one of the “television examples partaking fairly little of the comic book medium.” He is a hero who has super powers–which is enough to justify his inclusion under that heading–but he is also an agent of a government intelligence organization, which is the source of his powers and resources. Thus, he also gets a listing in Spy Fiction (Martini-flavored), which is where secret agents go. I believe the latter is a better fit. He could probably also be listed under Overt Operative–the main trope I was lampooning–though he isn’t as high-profile as many of the double Os. 
This. As a kid, my take was Steve Austin was Bond with the gadgets built-in, rather than picked up from Q Branch before every mission. This is also the flavor of the books, where Austin goes to exotic locals and works with other government’s covert agents.
I’ll admit, though, a lot of what I love about The Incredibles is the way it conflates the two genres - Syndrome is both supervillain and Bond villain, Mr. Incredible is both an overt agent and a secret agent. Very cool.
[spoiler]Another example would be Regent, who pretends his power is to cause involuntary muscle twitches in people to make them trip or fumble things. His actual power is to slowly take over people’s bodies and when he’s fully taken over use them as puppets.
Jack Slash from the same setting has the secret ability to tap into other parahuman’s powers and know ahead of time what they intend to do, which is why he’s so hard to kill.
Dragon is arguably a case; she pretends her abilities with technology are just due to her being a Tinker, but they are also due to her being an AI[/spoiler]
I recall coming across a fanfic where Superman admitted to having subtle mind control powers. Which is why no one realizes Superman and Clark Kent are the same, and why villains consistently try to fight Superman hand-to-hand, where he’s strongest.
“Even Lex Luthor straps on some power armor and tries to brawl with me. *Especially *Lex Luthor.”
It’s manga not western Super-hero, but the characters in JoJo’s Bizarre Adventure attempt to keep their powers secret, because knowing their power helps an opponent to surmise their weakness. In fact working out their opponent’s super-power drives much of the plot.