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On Batman Beyond, one villain was an Intangible Man who started losing control of his powers including his anchoring ability, so he started falling through successive layers of ground. The episode ends with the implication that he'll keep falling until he reaches the center of the earth. Depending on what other Required Secondary Powers he does or doesn't have, he may suffocate, die of hunger/thirst/old age, or be entirely immortal but his body would presumably keep falling even after that.
As seen in Batman Beyond, and the DCAU in general, a chemically-induced transformation usually leaves the victim without the ability to control the new form and the long term effects on the body. Examples include Mister Freeze's body rotting away except for his head, Clayface faced decomposition/liquefaction since his powers were granted by an overdose on a cosmetic product, Blight's radioactivity was growing in intensity and affecting his mind and the artificial skins used to hide it couldn't hold it back, and Inque's liquid nature made her vulnerable to simple water attacks (which would dilute her to the point where she couldn't hold any form).
One episode had Bruce showing off a Batman powersuit he had, but he couldn't use it because the strength increase put too much strain on his already unhealthy heart.
Another notable thing about the DCAU is that nobody has anchoring abilities. Many super strong and invincible characters get knocked around by punches and throws performed by much weaker characters. Even BATMAN once threw Superman across the room into some tables, although it only really surprised Superman that anyone would try it rather than hurt him.
Of course, Superman wasn't actively trying to use his powers there. He has shown anchoring powers before and since, so it's probably something he has to consciously make happen, and Batman caught him by surprise (Superman's so used to people shooting him, the thought that an unpowered human would use a martial arts throw against him probably never even occurred to him).
Of course, Batman already knew that. Considering that it's not like Superman doesn't keep his powers a secret, that's why he did that instead of punching him in the face with Kryptonite right off the bat.
Played for laughs in the Dexter's Laboratory episode "Don't Be A Hero" where Dexter tries to give himself various superpowers. He gets all of the powers but none of the Required Secondary Powers that make them effective. For example, Super Speeddoesn't automatically come with super braking and he ends up arriving at his destination later than he would have at a normal walk because he can't slow down fast enough and overshoots, around the globe.
Another episode had Dexter running late for school (he only had 30 seconds before the bus would show up), so he sped himself up 60-fold (giving himself 30 minutes). This lead to him having to move very slowly to avoid friction burns (even having to re-do his homework after accidentally setting it on fire), having to grab water droplets from the showerhead due to how slowly they were going, being unable to pour milk onto his cereal since he had to wait for gravity to take effect, and numerous other subversions.
Timmy Turner does the same thing in The Fairly OddParents. He learns his lesson and wishes for the secondary powers after the first few backfire.
Averted in Gargoyles, as the eponymous beasts, despite having wings, don't have any of the Required Secondary Powers necessary to enable flight, and thus can't actually fly (they simply glide). Dr. Sevarius notes at one point that the amount of energy the species uses for all this near-flight still requires the equivalent of eating three cows a day. He theorizes that their daytime stone forms may actually be a Required Secondary Power themselves, used to absorb solar radiation to provide the necessary energy for their aerobatics. The gargoyles are sometimes seen operating after a day spent indoors or in bad daytime weather; Word of God has said that missing a day's worth of solar radiation for a gargoyle is equivalent to skipping a meal. They'll have less energy, but it won't be very noticeable.
Another Required Secondary Power is the low-grade Healing Factor that seems to function on gargoyles when they're asleep; this, too, may be linked to Sevarius' "energy-storing hibernation state" theory. This secondary power is presumably the reason that the stone-destroying action of plants, lichens and weather didn't cause any disfigurement during their thousand-year enchanted sleep.
Bunnie Rabbot from Sonic Sat AM would have had the same problem, but the writers never discussed it. Since the interrupted process was supposed to transform her entirely into a machine, it's presumably pure luck that the half-way state she is stuck in is organically viable, or a safety device to prevent her from dying during the process.
One episode of the cartoon had her jam the jaw of a massive, dinosaur-themed mining robot open. Either she actually has Super Strength and never realized, or there's more of her that's roboticized than what's established.
Some fanfic authors have used the idea that the build up of toxins from the robot parts could be fatal. The actual comics used a similar "her stuff is killing her" at least once, which led to her getting a revamped look, and establishing she can't be "cured" ever. Her new cybernetics were established as drawing on her own energy, and that overuse could kill her. Following the reboot, it's not clear how her limbs work now.
Most versions of Sonic have him as a Big Eater, and note that his sneakers are specially designed to reduce the problems with friction. Occasionally other secondary powers are alluded to, and on occasion he has learned to use them for other means (the Sonic the Comic version noted that part of the reason he was so tough was that he could vibrate the particles around him to provide a forcefield against air friction and direct damage).
There was an advertisement/comic about Sonic that stated that his sneakers were, in fact, "frictionless". Which, while solving the problem of his shoes bursting into flames, creates the new problem of how he gains any traction, and thus is able to move at all... or stop, for that matter.
The idea of the sneakers protecting Sonic from friction was a plot point in an episode of Adventures of Sonic the Hedgehog. Robotnik's robots stole the shoes, leaving Sonic unable to use his speed.
Cross-county skis actually hold the answer to this: fish-scale skis, in which the bottom of the ski is like a ratchet, with the front edge of each "scale" being a shallow incline and the back being a sharp slope.
In Loonatics Unleashed, Rev Runner's powers include Super Speed, Sixth Sense and "GPS Sense". While endurance isn't normally a problem for him, he once stopped to take a break while powering the Loonatics' holodeck on a bicycle.
The Venture Bros. have The Impossible Family, semi-Affectionate Parody of the Fantastic Four; Cody bursts into flames when exposed to oxygen, and merely burns painfully as a result. The Invisible Woman expy can only make her skin invisible (or rather, make it visible: it's invisible by default and she requires all her concentration just to look normal).
In Avatar: The Last Airbender, Firebenders don't burn themselves despite their fires coming from their bodies, but can be burned by the flame of other Firebenders.
This seems to be a matter of control, however. Skilled Firebenders have been shown to be able to at least deflect or disperse fire thrown by an opponent if prepared for it; part of it comes from the bender's method of manipulating their element in unconventional ways ("bending" of plants, sand, metal, and even human bodies, or adapting principles like redirection from other bending disciples). It stands to reason that an unskilled or careless Firebender could hurt themselves, but it's likely that they're taught extreme control and discipline from an early age (after all, if your kid could breathe fire, the first thing you'd do would be to make sure he or she fully understood how dangerous it is).
If Aang's first Firebending teacher is anything to go by, the very first lesson a Firebender learns is iron control, and any Bender that can't or won't learn is probably going to get exiled because of the danger they pose to others (remember that Aang ended up burning Katara because he decided control was boring, and learned his lesson because of it; now, imagine someone who's screwed up once or twice and still doesn't get it).
Actually, there are visible minor burn scars on Aang's palms and feet in the latter half of Book Three, as he's beginning to master Firebending.
An idea which is supported by the Nickelodeon site stating that Combustion Man's missing arm and leg were caused by misusing his own explosive power.
While maybe not required, the Airbenders seem to have resistance to wind burns and Earthbenders aren't bruised by their kicking and punching of rocks, though how much of that is kung fu magic or just bending power is left unanswered.
Aang has been shown to use a spreading motion while increasing his speed meaning he is likely moving air out of his way. As for how he can breath without said air it has also been shown that Aang has in impressive lung capacity.
It's possible all forms of bending utilize a development of the person's chi similar to telekinesis- for example it's not actually their foot hitting the rock but energy transferred to the rock by the kick. Or they simply don't physically connect with the target and there's a miniscule gap unnoticeable to casual viewing, which is supported by the fact that Firebenders don't create flames touching their skin, but hovering just above.
A sound theory, supported by Haru's actions in episode 6, where he's seen multiple times just twirling a few rocks in the air above his hands.
Also, Airbenders and Firebenders both seem to be resistant to extreme temperatures, or at least extreme cold; Iroh was dragged around in only his underwear the day before the winter solstice, Aang wore his signature light clothes at both the north and south poles and went swimming near an island with patchy snow on the ground, and Zuko exploits the fact that Firebenders require breath control to swim under water for a long time.
Also, since Air and Firebending are basically jet and rocket propulsion respectively shooting out of your hands, Airbenders and Firebenders seem to have some kind of anchoring ability to prevent themselves being thrown around by their own power.
Much like Firebenders and learning control, Earthbenders must also condition their extremities through training; they all go barefoot regardless of terrain and when Aang was training he would seriously injure his hand from punching actual stone. When Toph went for a pedicure, the ladies at the spa had to grind the dirt off of her feet with a metal spade. For most people, that would also take off a significant portion of skin as well.
Spyke from X-Men: Evolution had the ability to grow spikes from his bones, which he could hurl at his opponents. As a result, he was frequently shown chugging large amounts of milk to replace the bone calcium he lost.
Darkwing Duck: When a misfired particle accelerator gave Darkwing Super Speed, he caught fire from the friction when he first used it, and Honker had to treat his uniform with some type of chemical to prevent this. Worse still, the Super Speed also accelerated his metabolism so he aged at a hyper-accelerated rate. This was used as a plot point as the villain set up a trap that would make Darkwing Super Speed himself into a pile of dust.
Apparently, simply walking backwards really fast reverses the aging process.
The villain Nanosec in Transformers Animated aged to an old man after overusing his powers (He was back to normal for his next appearance, though, though it's implied that Slo-mo interceded with her Allspark-enhanced artifact)
Jimmy Neutron used a superslick spray to give his shoes Super Speed. While the effect of friction in the air is never discussed, he had horrible control of the friction on the ground and was unable to stop. He ended up as a pile of goo.
A sentient pile of goo no less. Apparently it somehow separated his atomic structure and blended them together while still allowing his organs to function.
An episode of Kim Possible had the title character (and Rufus) don a pair of hi-tech shoes that allowed her to run incredibly fast, so that she could fight an army of super-sonic robots. She had all the secondary powers associated with super speed, apparently, except the ability to slow down. Even while not moving, everything around her moved so slowly it was almost stopped. By the end of the episode, she was mostly back to normal, but couldn't hit the brakes fast enough to stop in Middleton.
This also brings up a few questions, regarding the time she spent apparently doing nothing for what was to her likely several hours, while those around her were shown to have moved.
Exactly how does Shego manage not to vaporize her own hands if she doesn't have a Healing Factor? (A popular idea in fanon.)
It would also explain how she survived the end of So the Drama.
The titular character of Danny Phantom has a bucketload of these. For example, he's clearly very hard to injure considering the number of buildings he falls off of or is blasted through with minimal damage to himself or his jumpsuit. This one is pretty reasonable, though, because the story wouldn't be very interesting if damage was realistically represented every time Danny gets blasted, punched, zapped or shot through a wall.
Considering his powers are derived from being part-ghost, it's entirely possible he may have some form of immortality.
Also applies to ecto-blasts, which punch through walls with ease but only smack normal characters around.
Actually, his ecto-blasts seem to avert this. It seems like they can blast through people too. One episode, "Flirting with Disaster", suggests that he holds back when fighting around (or with) normal people. He even says that since he knew that it wasn't really Valerie he was fighting in that episode, that he wouldn't hold back this time. He then proceeds to blast two of the robot's limbs off.
He has no lasting problems with being frozen from the inside out, and their only effect during their uncontrolled development is to make him feel very cold and move slowly. Nor does he have any problems channeling pure cold through his body during subsequent uses of the ability.
He clearly also has some variety of superhuman eyeballs which never get dry or irritated from speeding through the air.
Then again, the same must also apply to any speedster type.
All standard secondary super strength powers also apply.
A minority fan theory about cutie marks in My Little Pony: Friendship Is Magic. The mark signifies what a pony's special talent is, and is usually seen as limiting; i.e., if a pony's special talent is woodworking, woodworking is all they can do. The theory holds that, inversely, the pony is intrinsically talented at everything related to their main hub talent; so a pony whose thing is woodworking is good not just at engraving wood, but knows about different kinds of wood, the proper uses of all the tools and creative applications thereof, the properties of different kinds of stains and varnishes, and what you can do with all that sawdust when you're done.
This is actually supported in an episode where Apple Bloom made a potion that made her keep getting cutie marks. She was able to use all the skills like a master, which ranged from speaking French to taming lions to using a hula hoop like a helicopter. However, this becomes another example of Required Secondary Powers because she was spontaneously generating new talents at random and they were always on. Her tap dancing talent manifested late at night, waking up Applejack because she couldn't stop tap dancing, and when her French-speaking talent manifested, she could only speak in French.
This is actually explained quite handily by Twilight Sparkle. She says that all unicorns have a little magic that help them with whatever special talent they have, despite not being especially talented in magic. For instance, in Twilight's case, her special talent is magic, essentially giving her endless possibilities in using it. Even so, she has to learn the spells and master them, or risk a variety of negative side effects (For example, a failed teleport scorches Spike in "The Ticket Master", an animation spell goes spectacularly haywire in "Winter Wrap-Up", and the gem-hunting spell she learnt from Rarity in "A Dog and Pony Show" behaves slightly differently). She's explicitly shown studying to make sure she can cast her spells properly in "Boast Busters", and hints from later episodes imply that she also learnt some spells from other unicorns in her life, friends and family alike.
Athletic pegasi would need to be very sturdy to survive the rigors of high-speed flight (while at the same time being lightweight, a difficult equation). Rainbow Dash, an exceptional athlete, is capable of destroying an entire barn by crashing into it unprotected without any injury (makes you wonder exactly what she did to damage her wing later on - attack the moon?) and is holding her own in an iron pony competition against Applejack, who is herself a very accomplished athlete even by earth pony standards.
As demonstrated by Twilight in the season 4 premiere, controlling flight is not a very easy skill to grasp. Even when she does manage to get into a somewhat stable flight, she finds out the only brakes she has are the ground.
Rainbow Dash outright states that flying is more than just "flapping her wings", as she notes that flying in the sky at high speeds usually means you'll be running the risk of ramming into something, and unlike on the ground you don't just come to a halt (at least not vertically). For that reason she must be subconsciously aware of everything around her at all times. This also neatly explains why she seems so unfocused in most episodes; she's actually observing all of the background events as well, so she's not as focused as the other characters on the task at hand.
Ben 10 , as XLR8, rather than running, skates on the ball-shaped parts of his feet to cut off the impact-with-ground problems and manages to keep dust out of his eyes due to a built in windscreen. Both are presumably evolutionary traits shared by all Kinecelerans.
In Ben 10: Ultimate Alien, Fasttrack suffered an inability to slow down when running quickly in "The Eggman Cometh".
Most of Ben's super strength forms seem to come with the required secondaries as part of the package.
The phase shifter, which grants intangibility, is explicitly stated to work intuitively, allowing them to remain grounded without falling through the floor, see without light ignoring their visual sensors, talk without phasing through the air, and passing through some objects while being able to grab others. The only limitation seems to be that the thing has to be turned on for it to work, and most likely cannot be used indefinitely. Worries about breathing are irrelevant, since its intended users are giant robots who don't need such things.
The Apex Armor is an invulnerable suit of Powered Armor that also grants enhanced strength as seen when Miko wears it and beats up a bunch of Vehicons. It has no anchoring ability whatsoever, allowing Predaking to toss around Starscream like a ragdoll even while he's wearing it.
In Archer, Ray eventually becomes a paraplegic but gets mechanical implants to let him move his legs again. Unfortunately, since that's the only mechanical part he can't really do any of the superhuman feats a full cyborg like Barry can do, as demonstrated when he injured himself trying to push a car out of a ditch.
Cyril: You have bionic legs and you lifted with your back?
In Frozen, Elsa the Snow Queen explicitly states "the cold never bothered me anyway" in her song to explain how she could live on a mountain top in an ice palace in nothing but an evening gown made of ice magic, and not a particularly warm one at that.
In American Dad!, it was revealed that Roger has super speed so potent he can pull off ONscreen teleportation. One might question the amount of friction that would cause, except it was revealed a few seasons earlier that Roger's skin is flame-retardant.