Photon: Aun Freya, who has the power to stop time in a wide area around her, actually lacks the secondary powers to prevent it from affecting herself as well (although she still has the required secondary powers to make sure the part of the world she's affecting still moves with the rest of the world, etc.). It's up to Photon, who is immune to just about anything to go in, knock her out to cancel it, and usually to beat the everloving crap out of whatever scared her so much she used her power.
Pointed out by the author in Ghost in the Shell. He goes on to explain that this is why full-body prostheses, like those of Motoko Kusanagi (whose only remaining organic components are her brain and nervous system), are preferable. The manga points out that if someone were to get, for example, his arm replaced with a prosthetic, his biological body would still be subject to the strain of muscle fibers tearing where the arm is connected if they lift too much weight. Full-body prosthetics on the other hand have theoretically limitless strength (since it's now all a matter of technology), enabling them to jump huge distances (like how the Incredible Hulk does) and survive the impact of the landing (albeit the ground will take damage.)
The animated film however also goes into some detail regarding the drawbacks of such a body. In one scene, it's mentioned that a full body cyborg like Motoko has a much denser body than a non-augmented human, which means that in a body of water without the proper buoyancy aids or position on the water, she'd sink to the bottom like a stone, which clashes with her hobby of SCUBA diving. In another, one of the most famous scenes of the film, Motoko attempts to rip the hatch off of a Spider Tank. However, while she can hold onto it just fine, her body gives out before the hatch does, and she succeeds in tearing her own arms off at the biceps when the material her body is made of breaks from the stress.
Ed needs to get his automail updated by Winry should he get taller.
Like Ghost in the Shell above, automail isn't treated as super strong limbs, rather they are treated as super-durable limbs, as many Ed's (and many military models) are made of steel and other strong alloys.
Alphonse, as a soul inhabiting a suit of metal armor, has the advantages of Nigh-Invulnerability, but also the drawbacks. His great weight serves to anchor him, but also hinders him. He is unable to eat or sleep... but also has no need to. He cannot feel pain... because he is completely numb. However, while an inability to feel without nerve endings makes sense, for some reason he can still see without eyeballs, hear without eardrums, speak without vocal cords, and even move without muscles or feeling and equilibrium required to coordinate movement.
It's eventually explained why he can still remember things without a brain: his soul is still "connected" to his body and mind which is on the other side of the Gate (and still aging).
Al and the other animated armors can move without muscles because his soul is infused into the armor. During Ed's fight with Number 48, 48 shows Ed the blood seal on the inside of his helmet. After some fighting Ed knocks 48's head off and thinks he's won because the part of the armor the seal is on is no longer connected to the main body. However, it's revealed that he has another seal on the chest of his armor, but after Ed uses a variant of Scar's disintegration to destroy part of 48's armor, the severed torso with the seal is no longer able to move its legs or defend itself against Ed.
Similarly, when Barry the Chopper's armor is destroyed, the piece with the blood seal on it can still talk, hear, see, and move (he can't move a lot, but he can move), but the rest of the armor can't.
The speaking part is actually lampshaded a bit, in that Al's voice has not changed since the incident. In The Movie for the 2003 anime, Conqueror of Shamballa, Al has gotten his body back, and grown up to the age he was in the series, and as such his voice is deeper. Oddly, when he gets his soul temporarily shifted to an identical suit of armor on Earth, he sounds like a nine-year-old again.
Likewise, the 2003 anime shows that when Lust scratches Al's blood seal, he seemed to be in pain.
In theory, it could be that the armour itself replaces his retinas and eardrums - he sees and hears the light and sound waves that interact with it. Presumably this would mean that he doesn't see (or interprets as being black) anything the colour of his armour, as that light is reflected rather than absorbed.
Alchemy outwardly seems to change objects from one state to another, but the process is basically breaking things down and rebuilding them, not outright changing them as-is. This is why Scar can only destroy things with his "alchemy": He does not know how to rebuild things once he "breaks them down". Until the end of the series, where months of studying his brother's notes allows him to apply the "rebuild" tattoo to his other arm - which comes in very handy during his climactic fight against King Bradley.
The above reason is also why Alchemy is seen as a science more than magic in the universe; it's simply a reaction one can induce, but not knowing the components you need nor how to assemble them into the end form means you, at best, end up doing nothing and, at worse, end up with a horrifying pile of junk that may or may not be throbbing. This is why State Alchemists have specialties; they don't know formulas outside of their purview.
The most evident example would be Sloth. Why? He has Super Speed, despite his size... and he's still faster than Lust and Wrath, turning into an ultra-fast wrecking ball. Unfortunately he has horrendous maneuverability and can't easily stop himself.
Brook is basically made out of these. He ate the Yomi Yomi no Mi (Revive-Revive Fruit), which allowed him to return to life once after he died. The ship he was on when he died was in a dense fog, and consequently it took him a year to locate his body and revive, in which time his body had decomposed until all that was left was a skeleton with an afro (strong roots). Fortunately, the fruit's powers also provided him with everything he needed to survive; he can move without muscles, see without eyes, hear without ears, speak (and drown) without lungs, eat without a stomach, use a toilet without bowels (Luffy asked), etc. Then we have his actual powers: in life he was over 8 feet tall and pretty strong (if not super strong). He maintains that same level of strength and can even increase it with time, but now his body is a mere fraction of the weight, allowing him to leap incredible distances and run across water. It turns out that all of his secondary powers are a result of a special energy given off by his soul, and post-Time Skip he's learned to channel this energy for all sorts of supernatural effects, from Astral Projection to Mass Hypnosis to a weaponizedGhostly Chill in fire form.
Luffy can bleed so much without dying because one of his secondary powers is a circulatory system that can make extra blood instantaneously to pump into his stretched out limbs. In fact, his rubberized organs, bones, and indeed every single vital part of his anatomy is the only reason he is able to withstand the stresses inherent in his Gear Second Super Mode. According to Rob Lucci, if anyone but Luffy were to use something like Gear Second, their heart would explode.
The two basic forms of Haki are this: Observation Haki allows you to be so in tune with your surroundings that you can sense what's about to happen, and Armament Haki allows you to coat yourself in a suit of armor. Unfortunately, being able to predict what's going to happen doesn't do you much good if you can't stop or avoid it, and if someone is powerful enough to break your armor, what's the point of having it? Boa Sandersonia and Boa Marigold, respectively, learned that the hard way when they took on Gear Second Luffy.
Logia users seem to receive a lot of secondary powers too, such as Ace, Akainu, and Aokiji, and Monet being temperature resistant, Kizaru having reflexes fast enough to keep up with his light speed movement, and Smoker being able to constantly smoke two cigars without organ trouble.
Logia users also have the secondary power of turning their clothes into their element of choice as well, seeing as none of the Logia users are left naked when they turn into their element.
Notably averted with the Op-Op fruit, or at least its more medical abilities. As a child Trafalgar Law originally couldn't heal anyone with it because he needed to use actual medical knowledge. The fruit only lets him control everything within his "Rooms"; he has to know what to do with it too.
Luffy also was an aversion since it took him years before he reached the skill level we first see in the manga. In the flashbacks when he tried to punch something his fist would bounce off and he'd sock himself in the jaw due to recoil and lack of aim.
Played for Laughs with Kanjuro, who ate a Devil Fruit allowing him to make real whatever he draws, be it objects (like ladders), animal (like a giant bird) or even food (like a salad). There's only one problem: He can't draw for shit, so his ladders end up difficult to climb and oddly shaped, his bird is an abomination that can barely fly, and his salad taste awful.
Ichigo's speed increase from his Bankai lacks one notable secondary power: namely the ability to withstand his own speed. His first use of Bankai almost causes his own bones to break towards the end of the fight. He has to toughen up before he can get over that particular limitation.
Word of God also states that the reason Ichigo and Renji can throw around their huge swords with no effort is because the swords don't weigh anything to them as they are a part of their soul, but they sure as hell weigh a lot to the person on the receiving end.
There's also the scene where Mayuri Kurotsuchi inflicts a drug on Szayelaporro that increases his perception of time, resulting in the world appearing to slow around him, without actually granting him super reflexes so his body can keep up (Mayuri mentions that he usually dilutes this particular drug). As a result, poor Szayelaporro can do nothing to stop Mayuri from stabbing him in the heart, despite seeing it coming for what to him seems like centuries. By the end, Szayelaporro is begging for death.
Required Secondary Powers also proved key to defeating an Espada, Barragan, whose power was that his touch could rot and decay anything. His opponent, Hachigen, worked out that he had to have a secondary power to keep the rotting touch away from his own body. Hachi exploited that fact by warping his own decaying arm inside the Espada's body, causing Barragan to rot away from the inside out.
When training to use his Fullbring, Ichigo needs to undergo intense endurance and strength training, as his time spent as a Shinigami did nothing for his physical strength which his Fullbring needs.
Captains and Lieutenants also are given power limiters when in the human world and compress their swords to more manageable sizes. When Aizen (after achieving near-Physical God level of power) approaches a human without one and Grand Fisher fights Issin Kurosaki, we find out why.
Kenpachi Zaraki's Bankai drastically increases his strength and ferocity, but he eventually destroys his arm from the force of his sword swing because his body has not had a chance to adapt to his new ability.
The weakest member of the Ginyu Force has the power to stop time. However, he can only do so for as long as he can hold his breath and maintain the proper concentration. Considering how out of shape he is, this isn't long.
Fridge Logic dictates this is why Oozaru form increases a Saiyan's strength and ki ten-fold. Growing to giant proportions allows them to access additional strength and ki, which would be needed to prevent their body collapsing under its own weight.
Many characters of Dragon Ball and Dragon Ball Z have super anchoring abilities as addition to their strength, otherwise they will blow themselves backwards when they use an energy attack. This is especially noticeable with Tao Pai Pai, in his Curb-Stomp Battle with Bora. He holds onto Bora's spear, who is unable to even move it one bit, not even upwards even though he should by all means be able to lift Tao Pai Pai upwards as well. Fridge Brilliance comes into play here, these characters fly by pushing ki in the proper directions. So presumably they could do something similar to hold themselves in place.
During the Buu Saga, Gohan teaches Videl ki control and flight. However, when the Z-Fighters fly off in search of Babidi's spaceship, Videl eventually has to bow out because she can't keep up, and can be seen shielding her eyes from the wind with her arms. This seems to imply that the energy aura put out by DBZ characters during high-speed flight takes care of all the minor concerns like wind, friction, etc.
Training is needed for the characters to breath in low oxygens environments, which is how they can fly so high without passing out. As a kid, Goku got dizzy and lost of breath when he first went to Korin's Tower and then Kami's Lookout.
Fighters are apparently able to control the amount of destructive force a Ki attack causes when it hits something other than an enemy, otherwise by the end of the first third of the series they wouldn't be able to use Ki attacks at all as any Ki blast strong enough to hurt any opponent close to their own level that missed or was dodged would blow up the planet they are fighting on when it landed.
Namekians have extremely sharp hearing, able to hear people talking from hundreds of feet away, even in a crowded stadium. Yet, they don't experience any discomfort from loud noises, unless you count whistling, showing that they can control the sensitivity of their hearing.
Goku has a powerful sense of smell that is as sharp as a dog according to Goku, yet he isn't bothered by strong smells any more than a normal person outside of Bacterian, who had never bathe a day in his life and can cause even a normal person to nearly faint, showing that Goku can filter out what he's smelling. He also has sensitive hearing, although nowhere near as sharp as a Namekian, given that he can hear people whispering behind his back and through walls, but loud noises don't get to him.
Almost all the characters in the series are Physical Gods capable of destroying a planet with little effort, yet they can pick up an egg without breaking it and be hurt by far less powerful people. They have to train themselves to be gentle. When Goku returns to Earth after being in space for over a year, he sent his wife flying with just a pat on the back. Their Ki also acts as a type of shield that must be consciously activated or raise, otherwise even a weak energy blast could pierce their skin.
This actually gets Deconstructed humorously in Dragon Ball Super. While Vegeta is able to control himself enough to handle most day-to-day activities and interaction, he can't crack an egg because even when using every ounce of his self control,eggs just shatter in his hand from the pressure. This is also toyed around with when it comes to LordBeerus. While he CAN show self control enough to interact with mortals, he doesn't always see it as important since he's a God of Destruction anyway. Thus you get scenes of him tossing people around like fleas when he turns in his sleep and destroying nearby planets with a sneeze.
All the characters also have good emotional control, yes even Vegeta. It has been shown several times throughout the series that strong emotions make people more powerful or loss control of their powers. When this happens, they can cause earthquakes, weather changes, or dimensions to shatter. An emotional slip like Vegeta going overboard on his temper could destroy the planet.
The characters can also move beyond light speed, yet still stop on a dime. This requires some training since inexperienced fighters have been shown stumbling or running into walls when they try to stop.
Being able to move and react at the super speeds that they do means that they also have to have an even more acute visual prowess that allows them to see other things moving just as fast. In more than one heated fight some of the lesser characters admit that things have gotten too fast for even them to keep up.
Cannon God Exaxxion goes into some considerable detail about what a 500+ ft. Humongous Mecha would need to be able to move around. The mechs use Imported Alien Phlebotinum gravity/inertial control devices to prevent them from collapsing under their own weight and allow their limbs to move at a reasonable speed, instead of feet they have invisible forcefields to distribute their weight to prevent them from crashing through the ground, because having actual feet big enough to accomplish this herculean task would look insanely silly (the fields are described as "invisible snowshoes" at one point), although at least that way bystanders would see them coming rather than being crushed underfoot by a robot that appears to be safely dozens of feet away. Aside from this, they're otherwise portrayed realistically and thus cause massive property damage to anything they get anywhere near simply by walking around.
Another contractor had bursts of super-speed, complete with friction resistance and clothes-extension. Unfortunately the friction-resistance only worked on air: Cue nastiness from Newton's Third Law as he ran into some raindrops at a speed faster than a speeding bullet.
There's also an episode where Hei faces down another Contractor with powers like his. When they grab each other, they form a complete circuit, knocking each other back but not producing a lethal shock.
This is far from the only fun the show has with his powers- most of the issues listed above are addressed simply by requiring something to conduct electricity. Plus, that's the only way he can control the path at all; shocking someone through a puddle of water on the road also blew out a nearby streetlight, for example. The finale addresses the manipulate electrons = manipulate matter issue, too. Turns out that in the right place, BK-201 is an outright Reality Warper.
Nancy Makuhari (a.k.a. "Miss Deep") of Read or Die possesses the power of intangibility, but is unable to breathe while using her powers, as air passes through her lungs while she is intangible. This presents the very real danger of drowning while using her powers underwater.
This is referenced in Psycho Busters when lead Kakeru wonders whether Kaito ever gets burned by his own flames. He then answers himself saying "Nah! He must have the impervious-to-fire power!". Kakeru later sees Kaito turning down a coffee saying his tongue is sensitive to heat.
Accelerator in A Certain Magical Index has a rather interesting required secondary power: mathematics and spatial relations. Yes, without them he could probably deflect anything anyone sent at him but he couldn't really aim. Vector control requires him to be able to figure out what to actually do to get the result he wants. Post Heel–Face Turn he's notably weaker because of some brain damage.
In fact, it's mentioned that most powers, if not all, are based on this, revealing the reason why the ability users have to study extensively to be able to get more powerful.
Some of the others are brought up in the A Certain Scientific Railgun side story. Range and accuracy are the limiting factors of Kuroko's teleporter abilities (any objects intersecting with things she had teleported are explicitly stated to be displaced). Mikoto uses the heat generated from her electrical abilities on two separate occasions, once to cook an opponent using a non-conductive barrier and another time on a smaller scale to cook rice in a metal canteen when the stove isn't working. In the anime Uiharu mentions a specific lack of required extras. She has the power to prevent things from changing temperature but her hands can only tolerate a normal range of temperatures limiting the potential for its use (though she's great at keeping take-away warm). Touma also has some going for him otherwise attacks like Mikoto's railgun would still be lethal as momentum keeps the projectile going even after her power has been negated.
Shizuri Mugino, the Meltdowner, can fire laser beams and create energy constructs like shields, but is not immune to them, leading to Shiage Hamazura tricking her into blowing herself up.
Notably, she seems to be the only Level 5 without any of the Required Secondary Powers necessary to handle her own ability, as not only do her beams require her to take a few seconds to precisely aim lest she destroy her own body, (as seen when she blows off her own arm when fighting angry) she can't even use her power to its full potential because her mind subconsciously suppresses its full strength.
Maria Kumokawa can increase the centrifugal force her movements generate, greatly enhancing her Dance Battler style. Since she does not have enhanced durability, she rarely goes over double the force, to minimize the chances of her breaking a bone or otherwise injuring herself.
According the the backstory of Zeta Gundam, Transforming Mecha are only possible, or at least practical, due to a revolutionary variable-friction magnetic coating on their joints that was first used by the original RX-78 series Gundams. This allows them to change in a snap. Without it, their joints would either be too rigid and their Transformation Sequence would take hours, or else their limbs and other moving parts would constantly be flopping around and falling out from under them. Later, it was later revealed that the Movable Frame pioneered by Kamille's father also made it possible as it created a skeletal frame for the suit to move with (This is also Truth in Television as it also helped create modern day Gunpla.)
There is also the idea of beam rifle technology. Mobile Suits initially had power generators too small and weak to use beam weaponry like a battleship could. However, the creation of the energy capacitors (or e-caps) allowed a beam weapon to gather energy within a battery and all it needed to fire was just a little bit of energy from its generator to fully unleash it. This is what made the Gundam so fearful.
Similar to the above, the various signature Transforming Mecha of Super Dimension Fortress Macross and its sequels employ 'Energy Conversion Armor' which uses metals and technologies reverse engineered from the eponymous Macross itself (termed 'Overtechnology'). This armor can absorb energy and use that energy to reinforce it's own structural integrity. According to the various supplementary materials of the series, this is what the energy output of the Reaction Engines is used for when not being 100% committed to thrust. Thus when in Battroid (giant robot) mode, standing on the ground, with 0 thrust, 100% of the engine output is going towards telling the Square/Cube Law to take a hike.
In Naruto the Fourth Hokage's "Flying Thunder God" technique lets him teleport to within a certain distance of a seal which he puts on weapons and enemies, thus avoiding Tele Fragging by only teleporting to places likely to be close to open space. Likewise Tobi once implied that he can detect things (or at least people) from great distances which would probably explain why he never teleports into random objects.
In a case of Fridge Brilliance, the ability to warp to several targets at once within seconds with the jutsu would require a good dose of Hyper Awareness. Otherwise, the user's perception of time and space would be screwed up badly. Worst case scenario, if the user fails to do this, their bodies could be wrecked.
It's stated that the Super Speed charge the Chidori is used at would make it impossible/impractical because it's so fast that it causes a tunnel vision effect if Kakashi and Sasuke didn't have their Sharigan eyes to speed up their reflexes. The same goes for Kiba and Akamaru's Dual Wolf Fang (which is even harder for them to see while using since it also has them spinning the whole time), so they need to have Akamaru piss on the enemy beforehand, so they can find their target by scent.
The sharingan itself has a similar problem: it grants the user superhuman perception but not superhuman agility. Sometimes a sharingan user can predict an attack and see exactly where it's coming from, but if their body can't keep up with their opponent they still won't be able to dodge/block in time.
Another example is Naruto's Rasenshuriken jutsu. At first his own arm would get busted up due to recoil damage, since it's a Rasengan-based technique and sits on the palm of his hand. After he gained Sage mode, the enhanced chakra gave Naruto the extra powers he needed to be able to throw the damn thing.
Also, most of his Rasengan techniques require this. Due to his poor chakra control, he relies on his clones to assist in properly forming even a basic Rasengan. He eventually removes the need when obtains a different secondary super power, the ability to form chakra arms with the Kyuubi's chakra.
Naruto's Healing Factor also qualifies. It's based on rapid mitosis, which shortens his life every time he uses it. However, he has longevity on his side- members of his clan are very long lived, so he can still live to a ripe old age even after having his skin burned off multiple times.
In fact, every Nine Tails Jinchuriki has been from his clan, precisely because they have the secondary powers to handle it.
Sakon and Ukon's ability to fuse their bodies with each other or other people requires them to be able to greatly manipulate the structure of their own body in some other ways, including healing themselves.
Susanoo generates a very strong Force Field, but it lacks anchoring (its user has been both knocked into another room, although not injured, and nearly sucked into the mouth of a giant monster) and at least slightly air permeable (an acidic mist was able to get through it, albeit it's still better than being unprotected).
The databooks state that the Earth technique to burrow underground has the user act as a human compass to keep track of their location and sense what's above so they know where to attack when coming up.
Mabui's ability to move a target from one location to another at the speed of light is largely limited to inanimate objects. For a living being to survive, they either need to have advanced self-healing, like Tsunade, or have Nigh-Invulnerability like the Third Raikage.
Kimimaro's ability to generate vast quantities of bone and project it from his skin as weapons and/or armor would necessarily require him to have some kind of healing factor so he doesn't hemorrhage to death every time he uses it.
Tailed Beast Transformation requires the cooperation of the tailed beast, or else the technique will backfire (possibly hilariously).
Kabuto's Sage Art: White Rage Technique acts as a flashbang combined with producing enough noise to make the air oscillate from the vibrations, blinding and paralyzing the opponent. He must use his snake-like cornea to block out the light and Suigetsu's Hydration Technique to liquefy his organs so they can absorb the sound.
In Claymore, when Clare awakens while fighting Rigaldo, she cannot control her speed and winds up running into more than a couple buildings.
Those Claymores who are known by the Organization to have shape-altering abilities are issued special uniforms that can stretch to accommodate the changes.
Durarara!!'s Shizuo acquired Super Strength pretty early on in life, but not the physical resistance that usually goes with it. The end result was that he spent as much time tossing cars as he did in the hospital from the resulting fractures until around high school.
Subverted with Zelgadiss in Slayers, a human/demon/rock golem chimera whose Nigh Invulnerability comes from him having skin made of stone (and hair that resembles steel wire.) Due to his "monstrous" (in his opinion) appearance, he's willing to lose his supernatural powers as long as he can become fully human again.
The various physical laws that Digimon break (size-shifting, thermodynamics, etc.) can be explained by the fact that their world is a big computer program. How they do it in the real world, however...
The franchise dances in and out of addressing some of this by having the Digimon, particularly in the Adventure continuity but also seen in Tamers, exhibit high amounts of hunger and sometimes the inability to transform or fight when hungry. Thereby implying that they burn vast amounts of energy to perform. Additionally, getting hit with large attacks reverts them to their base level and leaves them groggy and exhausted until they can recoup their energy.
It is assumed that the superstrength of the vampires in Hellsing comes with a limited form of telekinesis to deal with recoil. It's the only way that Seras could fire a gun that weighs three times as much as she does on full auto without bracing against anything without going flying.
The fact that one enemy's force field was not air-permeable was the key to her defeat in Dragon Half. Mink breathed fire at her until all the air in the bubble ran out.
Being omnipotent without the omniscience to deduce how your changes will play out is a significant plot point in Serial Experiments Lain.
Fridge Brilliance dictates that they should be able to make themselves omniscient, at least if they are truly omnipotent. Makes one wonder why they don't do it... Maybe it just never occured to them?
Chirico from Armored Trooper VOTOMS has a powerful Healing Factor but still feels pain the way a normal person would. As he result he has serious psychological problems due to suffering through the agony of countless things that should have killed him, like being cut into pieces or burned alive with high octane fuel.
In Mahou Sensei Negima!, the main downside of Negi's RaitenTaisou is that Negi doesn't have the required secondary powers, and must control himself through extremely advanced wind magic, which, due to requiring him to previously "mark" the destination and making him unable to actually react to change course mid-air, make it very possible to counter it by just obstructing the way between Negi and his target. Raiten Sousou, its upgraded version, provides the required secondary powers.
Several of the heroes in Tiger & Bunny. The strong, and/or fast ones (Kotetsu, Barnaby, Antonio) are durable enough to use those skills without injuring themselves. Karina and Nathan are likely to have resistance to their own elements, and Pao-Lin explicitly states that a taser won't work on her. Possibly odd example in the case of Lunatic who can create fire in his hands for use in his crossbow, but his flashback in episode 16 shows that once he's set light to something (or in that instance someone) his fire can still harm Lunatic himself, as his father quite deliberately burnt young Yuri's face.
In High School D×D, Issei's power is having Boosted Gear, a Sacred Gear that doubles his power every ten seconds to the point that he can kill any deity whatsoever. The drawback however is that his stamina also gets drained because his body cannot handle the stress of his Sacred Gear's power. This leads him to undergo Training from Hell twice, once from Rias, and another one from Tanninim.
Either subverted or played incredibly straight in Shinryaku Ikamusume. It's eventually explained that the reason Squid Girl can pick up people and other heavy objects with her tentacles without losing her balance is that she can alter her weight with her bracelets, becoming heavy enough to anchor herself.
At first one might think that the armors in Saint Seiya protect the users from the opponents' attacks; in fact, the armor's main function is to protect the user's body from his own powers since a normal human body isn't able to resist such amounts of power. Of course Fridge Logic kicks in most fights since more often than not the characters end up half-naked.
In one episode of Mega Man Star Force, Cancer Bubble grew to a prodigious size. However, as he didn't become any heavier or more powerful, he was still a pushover for Mega Man.
In Medaka Box, part of Mogana Kikaijima's training as a swimmer gives her superhuman lung capacity, allowing her to hold her breath for up to a month or use her voice as a weapon.
In Is This a Zombie?, Ayumu Aikawa is a zombie, meaning he can survive and recover from nearly any injury. Unfortunately, he can still feel pain. He also has super strength, but since his body is not super durable, he can break his own arm from the force of his own punch.
From the same part, Johnny Joestar's stand Tusk and its subsequent ACTS allow him to shoot his fully grown fingernails with the velocity and piercing capabilities of a bullet. It's also a good thing that Tusk is courteous enough to actually regrow said bullets within a few seconds (or a few minutes if he fires a much stronger shot), otherwise he'd have to wait from anywhere of four weeks to six months for his nails to come back and "reload".
Earlier on, Vanilla Ice (no, not the real one, but named after the real one) can turn into an invisible and mobile Sphere of Destruction, which removes from existence anything that touches it. Polnareff and Iggy, who have to fight him, soon discover that, because the ball is invisible, Vanilla Ice cannot see when in this form, meaning he can only attack blindly and has to emerge from it to understand what's going on.
Diavolo's stand King Crimson can skip time by up to ten seconds, essentially eliminating the first step in causation by forcing everyone and everything to unconsciously act out the time it "erased". The reason why its such a massively overpowered stand is because of its sub-ability called Epitaph, which lets him see the time that it was about to erase, thus letting him prepare and set his actions accordingly. Without Epitaph, Diavolo would be confused and disorientated just like every other character (and a first-time reader, no doubt) who fights him, as it would look roughly similar to a grand-scale Teleport Spam.
To utilize a Stand at all requires one to have the proper amount of Heroic Resolve (or the villainous equivalent thereof) to get it to do what you want. This has been brought up a few times when weak-willed people somehow manage to gain a Stand that they then can't control (such as Masozo Kinoto and Cheap Trick) or can cause the Stand to actively reject its User and do them harm (such as when Holly Kujo acquired her unspecified Stand through her shared bloodline with DIO/Jonathan Joestar that created a horrible illness in her that slowly started killing her).
Get Backers: Himiko Kudou's claim to fame is using various types of perfumes for combat. These range from a degenerative perfume that regresses the mental capacities of the victim, a flame perfume that sets the air on someone's lungs on fire, and so on. Her "ultimate" perfume makes her able to attain greatly increased speed (multiplicatively, by the number she smells her perfume) by exerting more force to her muscles and reactivity. However, she does not have the required powers of infinite muscle/bone durability, and so her entire body nearly breaks down when she used it. She never did use it very much precisely because of this reason.
She does have a required secondary power for everything else: since her very power depends on people breathing her poisonous perfumes, she had developed a method of breathing by sensing which air is safe enough to breathe (which basically entails a heightened sense of air pressure reading). As proof, her own sweat and body odor is a mild hypnotic psychoactive "perfume". The fact that she herself isn't affected by it is proof of her secondary powers (or at least demonstrated tolerance to her own poisons).
Brynhildr in the Darkness: Kotori's teleportation resets the kinetic energy of the target, which is how she can rescue someone from a multi-story drop without them splattering on contact with the ground.
My Hero Academia acknowledges this trope by including the main power and all the mechanisms that allow it to function within a single denomination (Quirk Factor). It also plays with the trope by often giving the secondary powers limits of their own.
Izuku Midoriya's body still can't keep up with the raw power granted by One For All, even after training with All Might for months and gaining a muscular physique just so that his body wouldn't explode in the first place. All Might himself never had this problem due to having his own required secondary power of a strong enough body that could withstand One For All from the beginning.
Katsuki Bakugou is resistant to his own Having a Blast powers, but not completely immune. If he goes too far with it, his arms go numb.
It's also worth noting that Bakugou creates explosions through nitroglycerin-like sweat, which he is capable of secreting from his hands at will.
Similarly, Shouto Todoroki can create ice and fire while not being affected by burns, but is not immune to either frostbite or overheating, which happens if he goes too far with either power but not the other (he can avoid this by simply using both elements in conjunction so that his body temperature is always regulated, although this also means that each element ends up weakening the other due to them being mixed).
Tenya Iida is built like a bodybuilder, so that the upper half of his body can keep up with his literal engine legs.
For whatever reason, Minoru Mineta himself is the only thing that's immune to his own sticky hairballs. Otherwise, they would just get stuck to his hands.
Denki Kaminari can generate his own electricity, but while most of his body is immune to the electric currents, his brain is not as it can temporarily short-circuit for some reason. At the very least, it is not completely vulnerable, or else it would be dead fried by now.
Momo Yaoyorozu can create any object as long as she has an in-depth knowledge of its atomic structure, which means anyone with an I.Q. below genius-level would not be able to create all the cool, complex technological stuff like firearms and computers without having to look at it in a picture in the first place. Also, all the mass she needs to create those things come from ingested food, so "molecular conversion of fat to mass" ends up being one of her required secondaries.
Mirio Togata has a form of phasing, which lets him become intangible and pass through solid objects. However, he lacks many of the secondaries that would allow him to otherwise function normally while using his power. When intangible, everything, including light and oxygen, passes through him, meaning he can't see, hear, or breathe while using his power. He can't easily keep his clothes on, either. If he goes far enough he can even sink into the ground, though his body does eject itself from whatever he's inside at the time to avoid a Tele-Frag. Mirio weaponizes this aspect to enable him to move quickly by sinking into the ground and positioning himself to be shot a certain way when becoming tangible again.
Hero costumes are often designed to invoke this, reducing or nullifying the negative effects that tend to come with every Quirk.
The title character of Cyborg 009 and the rest of his fellow 00 cyborgs are specifically enhanced to be able to withstand the acceleration of using or being carried through 009's Acceleration Mode. It's explicitly mentioned that if 009 takes normal humans into Acceleration Mode, he could easily end up killing them.
Supplementary Materials note that using 3DMG requires very high amounts of coordination and balance (borderline-acrobatic levels) to use, much less pull off fancy maneuvers that Survey Corps veterans are seen using, as well as high leg strength, good aiming skills while mid-flight to actually land grappling hooks, and Nerves of Steel to keep it all together and not lose balance when disaster strikes (it's even stated that instructors will cut the cables on recruits to test their mettle). Also, one would presumably need to not be afraid of heights and be motion-sickness resistant.
Titans are noted to have an extremely high body temperature, with the Colossal Titan in particular having heat generation as a defensive and offensive ability. The humans that "pilot" one of the intelligent Titans are only slightly warmer than normal when exiting, indicating that they are able to regulate their body temperature to avoid being cooked alive.
The lack of these is what caused physical changes in the creatures eventually known as counterdragons in "Unlimited Fafnir" is what lead to their monstrous appearances, as their physical bodies changed to accommodate the powers they possessed. Iris shows this as she starts growing red diamond scales and changing her "Magic Staff" into a part of her body to use greater levels of the Catastrophe power she inherited from 'Red' Basilisk.
Many of the characters in Charlotte are afflicted by a lack of this, including the main characters.
Takajou has what he calls "teleportation", which is really just super speed. He has the buffed awareness to supplement it, but not the reflexes or control to stop himself or make fine movements while using it. In fact, he outright says he had to undergo a lot of physical training to make his ability even remotely useful.
Yuu can possess the bodies of others, but lacks the ability to control his own body or how long he's in the second person's. Once it's revealed that this is actually a side effect of his real ability, it's slightly less important.
Zigzagged with Shichino, who can pass through solid matter, and does have the secondary ability to control which matter, it seems. But he gets extremely fatigued after using it, which may be a lack of secondary powers, or may just be a lack of physical conditioning (the only time we see him use it is when he's in a prison so they can observe his ability, so he may just not have built up the physical endurance some other characters have).
Since magic in Lyrical Nanoha is based on complex mathematical equations, mages must have a very good and extensive mathematical knowledge. Before becoming a mage herself, Nanoha has been stated to be very good in math and Fate is stated to be good enough to be able to tutor Nanoha's older sister, who is a college student. Nanoha's skill set also required physical strength and endurance, as her most powerful spells are Wave Motion Guns that are explicitly stated to strain the body if used frequently. By Force, Nanoha can carry a BFG with one arm while carrying the rest of the cannon's equally bulky attachments at the same time.
In Myriad Colors Phantom World, Haruhiko shares Mai's memories and gains her martial arts skills in the process. Unfortunately, he's horrendously out of shape, so that knowledge doesn't do him any good as he lacks the strength, speed, and stamina to apply these skills.
Jaaku King from Futari wa Pretty Cure wields the Power of Destruction that allows him to annihilate anything forever. Problem is, he lacks immunity to this power and he is, in fact, slowly being killed by it. The plot of the anime was kick-started by Jaaku King destroying the Garden of Light and stealing the 5 of the 7 Prism Stones to use their power to wish for immortality before his inevitable death.
On the subject of Pretty Cure, many series have pointed out that their powers are based off of their mental states. The happier and calmer they are, the stronger and in control they are. Cure Blossom and Cure Happy have launched themselves airborne in a panic, Cure Bloom and Cure Egret have cancelled out their own forms by having a very bad argument and Karen Minazuki was refused her Cure Aqua powers at first because of her initial selfish reasoning.
Exploited with the ability "Sun & Moon: Paired Destruction" creates markers on two surfaces, one of the Sun and the other of the Moon. If the markers come in physical contact with each other, both surfaces will explode. Chrollo, upon stealing this ability, learns that the markers cannot be removed once deployed. He then deduces that in order for that effect to be possible, the markers must also grant invulnerability to all damage and deterioration until they explode. Chrollo then decides to use Sun & Moon more for its secondary ability than its intended one: He uses Sun & Moon to grant said invulnerability to his puppets, and, through a loophole, allows him to retain Sun & Moon even after the original user has died (ordinarily, he would lose the ability).note Chrollo leaves a Sun marker or Moon marker without its counterpart somewhere hidden and remote. Since the ability is still active, and because the thing he attached a marker to cannot be destroyed in any way, and thus the incomplete marker cannot be destroyed in any way, even through Chrollo's own power-copying limitations, Chrollo can be sure he can continue to use Sun & Moon for the rest of his life.
Discussed with the ability "Little Flower," an ability created by Genthu in which he can blow up anything he holds in his palms. Gon asks his mentor Biscuit how he can use that power without blowing up his own hands, and Biscuit correctly guesses that Genthru has to also create armor on his hands through his Nen, or life force. This brings up a further required power in that Little Flower consumes a huge amount of Nen, as Genthru has to expend some of it for the explosions and an equal amount or even more to protect himself. This means Little Flower can only be done by someone with large amounts of Nen, which Genthru happens to have.