"I am Shirahama Kenichi, an extremely ordinary first-year high school student who loves reading books and growing flowers. But, for some reason now, I'm locked in a desperate battle on top of a speeding bus!"
Takashi Komura, the main character of the anime/manga Highschool of the Dead, is a pretty ordinary average high school student, prone to skipping classes and accused by his childhood sweetheart of being lazy...that is, until the school's professors, then students, start being turned into zombies, and the aforementioned childhood sweetheart's current boyfriend starts turning into one. Takashi bashes his head in with a baseball bat.
Shibuya Yuuri, in the manga Kyou Kara Maou is an average high schooler, while he's suddenly summoned through a toilet seat to another world where he is the ruler of the whole thing. Again, average.
Kouji Kabuto from Mazinger Z was an ordinary student sometimes skipped classes, drove bikes and took care of his little brother. Then he found out his grandfather had built a Humongous Mecha and wanted him piloting it to save the world of a Mad Scientist. His friend Boss also counts: before Kouji moved to his school, his life was completely normal. If we check the sequels, Tetsuya and Jun from Great Mazinger averted this trope, but Hikaru Makiba from UFO Robo Grendizer did not. She was a pretty normal high-school student lived in a ranch and loved riding horse... until she found out the cute boy worked at the ranch run by his father was an alien prince in disguise and a Humongous Mecha pilot. Maria Fleed believed she was an ordinary high-school student, raised by her grandfather... until her grandafather revealed to her that she was the last survivor -as far as he knew- of the royal family from planet Fleed.
Tenchi Masaki in any of the incarnations of Tenchi Muyo!. Turns out he's an alien prince, and his family never bothered to tell him. Then there's Sasami, who tries to become one of these in the manga volumes. Being that she is an alien princess (and unlike Tenchi, knew all along), it doesn't quite work out. She should be glad that the goddess she's symbiotically fused with didn't decide to show up.
Tsukino Usagi, junior high student and reincarnated moon princess. And indeed all the Sailor Senshi.
In particular, Tomeo Hotaru a.k.a. Sailor Saturn, who when introduced is a small sickly girl who made friends with Chibi-Usa, only for us to discover that not only is she the host for the Big Bad of the season, Mistress 9, but is also the as-of-yet unawakened Sailor Saturn, the senshi of destruction and rebirth that Rei had been having visions of destroying the world. In the manga she then is aged back to a baby and adopted by Sailors Pluto, Uranus and Neptune only to age at an incredible rate when their presence is later needed by Sailor Moon.
Kei Kurono and Masaru Katou (and in fact all high school-aged characters) in Gantz are bona-fide Ordinary High School Students until they get hit by a train and resurrected to play the Gantz Game. They're still technically Ordinary High School Students after that, they just have superpowered combat suits and deadly weapons — and Kei is extremely good at using them.
Miaka Yuuki, Yui Hongou, Suzuno Oosugi, Takiko Okuda and Mayo Sakaki of Fushigi Yuugi all started out as examples of this trope.
Tohno Shiki in Shingetsutan Tsukihime, who even went so far to claim he was an ordinary high school student, when, naturally, he was anything but. Arcueid even comments on it. The best thing about Arcueid: she's being completely earnest without a trace of irony.
Kagome Higurashi in InuYasha. In fact, this trend was specifically mentioned in the Anime. "It's been a while now since this every day average school girl has been crossing back and forth between the warring states era and modern times!" Unlike many anime where this is eventually eliminated, Kagome retains most of her School Girl-ness, to the point of always wearing her school fuku in the warring states period of Japan, and never measuring up to Kikyo - her previous incarnation who was a Miko and is now half-alive and devours souls to stay that way. Like Sailor Moon's Usagi, her gifts are related to a jewel or crystal, and her greatest strengths personality-wise are her kindness, love for others, and ability to make friends. This can bite her in the butt with such characters as Kyoga the wolf prince who just doesn't take the hint, and Hojo, who like-wise can't take a hint.
The not measuring up to Kikyou is HIGHLY debatable considering Kagome succeeded at everything Kikyou failed at. Purifying the jewel, killing Naraku, loving Inuyasha, marrying and being a priestess at the same time. She is also canonically stronger and more powerful than Kikyou. The only problem is that neither Kaede nor Kikyou can be bothered to train her, despite the fact that they owe it to her. So kagome is forced to learn on the job and fast. And she succeeds at THAT too.
Ordinary or not, he has leashes on two of the most powerful beings in the area and can destroy the universe at will — or rather, holds the keys to the molly guard over the nuke button, as it were. And the third girl also trusts him to keep her secret from herself.
The animes didn't wait as long, being only one season each (compared to the Long Runner manga), and made all the Muggles abnormal in the season finale.
If you stop and think of it, there were only four Ordinary High School Students (Nodoka, Haruna, Misa, and Madoka) to start with, although exactly how involved they were varied greatly. Yue, for example, didn't know anything about magic but knew that Mana, Kaede and Ku Fei were some type of mercenaries who would be able to help fight monsters.
As of 34 volumes in, only two characters in his class are not supernatural, either due to the above list, training from another, or a pactio.
Amu Hinamori from Shugo Chara!, though in elementary school, is a good example. After she obtains her guardian characters, she ends up with a couple of friends and a somewhat reluctant membership of the Seiyo Elementary Guardians.
Koyomi Mizuhara (Yomi) from Azumanga Daioh is a subversion, in the ironic sense that not only is she really and truly normal (even — or rather, especially — compared to her friends), she actually gets to stay that way.
The main characters of both Yu-Gi-Oh! and Yu-Gi-Oh! GX, although in the latter case the high school is actually a training school for professional Duel Monsters players, changing the standard of "ordinary".
Subverted in Bleach. Main character Ichigo Kurosaki protests frequently in the beginning of the series that he's an Ordinary High School Student... who just happens to be able to see ghosts. This proves to be a crucial distinction.
Ichigo's more-ordinary friends do have an unusual tendency to turn out to be not so ordinary after all, including a girl whose hairpins can raise the dead, a huge foreigner with a demonic arm, the last remaining member of an ancient order of magical warriors, and the secret concealed by Ichigo's father's Obfuscating Stupidity he's a Shinigami.
In later episodes, a random classmate developed the ability to sense the spirit world, after showing no such ability before.
Takumi from Initial D delivers tofu in an old beater; and in the process, has learned drifting techniques that racers take years to master.
Sakai Yuuji of Shakugan no Shana. All extraordinary traits he has he owe to an artifact he received out of luck. Unusually, we never learn how long he's had it.
He knows about his powers, that his adopted father is a magus, and that there are other magus. He just didn't know that he has a Reality Marble or expect that he could get that strong, since what talent he had lay in what was regarded as one of the most useless forms of magecraft.
Mikan Sakura from Gakuen Alice who suddenly discovers she has a special ability called an alice and is admitted to the Alice Academy. Though she is younger than a high-school student at the time.
Shinji Ikari from Neon Genesis Evangelion is a very intentional Deconstruction. An ordinary student put in an extraordinary situation, Shinji faces a lot of issues and difficulties when facing off against the Angels, and because he suffers from a crippling lack of self-esteem and doesn't have any extraordinary abilities or skills, he's frequently out of his depth.
Light Yagami from Death Note is a perfect example of this trope, until it's derailed by the fact that he's both incredibly smart and megomaniacally insane. Though all indications are that said insanity would never have manifested had not been granted the ability to kill anyone just by writing down their name; during a Memory Gambit he's legitimately horrified by the notion that he could be the infamous serial killer Kira.
Yasuhara of Ghost Hunt puts an unusual twist on this trope. He was a relatively normal high-school student until the rest of the main characters showed up and kind-of absorbed him into their group. Out of the eight main characters, Yasuhara is one of only two characters who has no powers at all. though the other 'normal' character is actually just hiding his identity and amazing powers, though we don't find that out until the last episode. The twist? The series does not focus on him. In fact, he doesn't even show up until halfway through the series. He's there more to do the off-screen research for the group, which means that the assholish-yet-somehow-charming character who had been doing the research previously now gets more screentime.
Mai being a more typical example - she's the 'normal' girl interested in ghost stories who gets involved with the ghost-hunting group and early on wonders what it would be like to have psychic/spiritual/etc powers. Turns out she has quite a few.
Touma's passive negation power certainly makes him look like an ordinary student compared to people like his lightning-wielding Unknown Rival Mikoto under most circumstances. In their first onscreen confrontation, Touma protests to a sparking Mikoto that he's "just a Level 0" esper. Mikoto makes a compelling rebuttal in the form of a giant blast of (ineffectual) electricity. He's "Level 0" only because his power is impossible to quantify.
If you're looking for the truly normal students, there are Saten Ruiko, Hamazura Shiage and Wataru Kurozuma, who do not have the benefit of anti-magic or anything of the like, they really have no abilities. Just special abilities, since even normals can outdo espers and mages where it counts.
Almost all of the HiME from Mai-HiME start out at this stage (although a few of them are dead set on staying that way). Those that aren't (Midori and Sister Yukariko) were Ordinary High School Teachers.
Saya from Blood+ is an ordinary high school girl on the surface, but thanks to almost a lifetime's worth of amnesia, she has no idea of her vampiric abilities... until a Chiropteran shows up at her school and starts messing things up, and she's forced to kill it.
Rito from To Love-Ru wishes he was still an unremarkable Ordinary High School Student instead of the center of a complicated Love Triangle with at least half a dozen points on it, including three or possibly four Alien Princesses — Lala, Run, Lala's little sister Momo, and maybe Momo's twin Nana.
Taken to extremes in Code Geass. Lelouch is an ordinary high school student...who is an outcast prince, genius military strategist chessmaster, and all around Magnificent Bastard (with freaky mind-control powers) biding his time to jump at a chance to destroy Britannia. Kallen and Suzaku are inversions, being ace mecha pilots (with inexplicably superhuman physical abilities, especially Suzaku) for their respective sides who in the first few episodes come back to high school.
This can also be said of fellow student Nina, who starts the series as an above-intelligent but otherwise normal student and ends up a Psycho LesbianGadgeteer Genius. Shirley and Milly are also fairly normal, but start to really get wrapped up in events later in the series... really, the only character in their group of friends who stays absolutely normal throughout the show's run is Rivalz.
The Tower of Druaga. As Kai said about her hero king husband who slew a god and united two warring nations under one rule: "Even Gil was just a ordinary boy in love."
Kenichi Shirahama in History's Strongest Disciple Kenichi is even stated in the manga/anime to be completely ordinary and without talent for martial arts. His only talent is being a hard worker. Eventually they're able to beat skill into him.
A later manga episode lampshaded it. When the principal organized a contest of physical prowess among the classes one student immediately protested that one class had an unfair advantage due the presence of students with superhuman abilities. Ataru, Lum, Mendo and Ryunosuke agreed that those students had to be equalized... Only to realize too late they were speaking of themselves: Ataru was incredibly fast, Lum could fly (to be fair she's an alien, and on her planet it's normal), Mendo's arms were so strong he could break a bronze bell from the inside and Ryunosuke had Charles Atlas Superpowers!
Ouran High School Host Clubs Haruhi, who is the subject of a reverse harem situation, for reasons she doesn't understand. The normal(-esque)commoner put in a school of rich kids with trope personalities. She just wants to study. Lampshaded by the fact that she is only revealed as a girl at the end of the first episode.
Nanami from Kamisama Kiss starts out as one before being unwittingly turned into a Physical God before the end of episode one. Even after this she still tries to act like one and maintain the illusion that she is one.
Peter Parker, which was revolutionary at the time. A sidekick-aged protagonist?!
Inverted in Spider-Man Loves Mary Jane, however, in which Mary Jane — the protagonist — actually is an ordinary high-school student.
Doug Ramsey was a kid from suburban New York who was good at languages, and didn't know any different until he was informed by an acquaintance from the odd boarding school nearby that he was in fact a mutant with powers of... comprehending languages... and dragged out of bed in the middle of the night to come establish communications with a potentially hostile alien.
The Runaways were all normal teenagers... who in the course of a night watched their parents kill a young woman, discovered superpowers/super gadgets/a telepathic dinosaur, fought off their parents, and ended up becoming runaways living in an underground mansion.
Jaime Reyes, the current Blue Beetle in The DCU. One day he's just hanging out with his friends, the next he gets bonded to an alien symbiote, helps Batman save infinite universes, and goes missing for a year, yet he still manages to come off as more of a normal kid than 90% of other teenage superheroes in comics.
For a while Tim Drake was this being just a regular, although brilliant, kid who through diligent detective work uncovered the secret identity of the first Robin and through him Batman and the second Robin. Even after taking up the mantle and becoming the third Robin he still fit the mold for a good portion of his career; his change didn't come until Identity Crisis led to his father's death.
Mary Jane Watson of Ultimate Spider Woman was an Ordinary College Student when she began to develop her bizarre superhuman abilities, and continues to be one even as she tries to juggle a superhero career along with it.
In Time Will Tell, Jorryn is sixteen years old when she falls into the Shire. This happens, not during school, but during the summer holiday of 2001. Jorryn is only four feet and five inches, short, but taller than a hobbit. Other than that, Jorryn is a generic girl from some small town in the USA.
Sam Witwicky was just an Ordinary High School Student until he bought his first car. Turns out it was an alien robot.Who knew? His special quality is just being the great-grandkid of the man who found Megatron.
Subverted in Garth Nix's Keys to the Kingdom series, in which the protagonist essentially becomes the heir to the House (the "epicentre of creation", the denizens of which give our universe about the same casual interest as a rather exciting zoo) simply because he almost died on the right day. That's right kids. This kid essentially becomes God by nearly dying.
Bella Swan in Twilight. Until she falls in love with a vampire — or more to the point, the vampire falls for her.
In the lovely juvenile novel Wings by Bill Britain, the main character is an Ordinary High School Student who inexplicably develops a huge pair of fully functional bat-like wings.
The Animorphs. Ordinary middle/high school kids whose lives are changed forever when they decide to take a shortcut through a construction site.
In the Alex Rider series, British teen spy Alex Rider gets a lot of flak from his teachers after spending too much time "off sick" — though the obliviousness of everyone else does stretch credulity after Alex, having used a school trip to investigate a GM facility, escapes by jumping onto the roof of the coach as it leaves the now-badly damaged building. When he uses a toilet break as a way of getting on board properly, the teachers barely say a word.
Ben was this before he was Trapped on Draconica and in defiance of what almost always happens next, he stays ordinary. By the time he finds out that he has a unique power to travel between worlds, at the end of the story, Dronor says he has to take it away from him to make sure a villain never gets their hand on it again.
Tsuruhara Iori and Aragaki Koji in War and Snowflakes. Aragaki, it is revealed, is not so ordinary: he had been conscripted to be a titan pilot until a training accident made him unable to be a pilot, and left him with uncanny mechanical abilities.
The Exile's Violin: When the story begins, Jacquie is on her way home from school. The school itself is never seen because her life is blown up and she goes straight to vocational training, so to speak, under her foster father. Occasionally she'll reflect back to this time with regret and lost opportunities.
Played with inStrength & Justice: the story starts with Jeremy Itsubishi's role as a law enforcement cadet with Improbable Aiming Skills as his superpower. It's only after that we find out he's a high school student as well. Then he's pulled into the main conflict, playing the trope straight.
Live Action TV
Roswell had this as the main hook for the series (and helped pioneer the genre). Max in particular strives to as "average" as possible
iCarly on Nickelodeon has ordinary high school students hosting an internationally popular hit webshow.
The Vampire Diaries - Elena, Matt, Bonnie, Caroline, Tyler, Jeremy. This all changes when all of the characters start to develop their own individual identities.
Veronica Mars - a normal high school student...and a private eye.
Alex from The Secret World of Alex Mack. She even says "I was just another average kid until an accident changed my life" in the opening credits. It's also worth noting that she wore a similar outfit to the one described above on the day she was soaked with the chemicals that gave her superpowers.
Spellbinder - the main character, Paul, gets trapped in a parallel world during a school field trip, and his arrival is a catalyst that causes political upheaval in the otherwordly society. His friends Alex and Katrina have to juggle school as they work to bring him back.
H2O: Just Add Water - three, ordinary teenage girls suddenly realise they have the ability to turn into mermaids whenever they're splashed with water, and this is accompanied by elemental powers.
Scott Mc Call from Teen Wolf was an ordinary high school student (and asthmatic, no less, which severely curtailed his attempts to make the lacrosse team) until he was bitten by a werewolf.
Sabrina from Sabrina the Teenage Witch was just a normal high school girl until her sixteenth birthday, when her witch half manifested itself.
Maria, Kelsey, Clyde and Rani from The Sarah Jane Adventures. Clyde and Rani do have distinct talents, however- Clyde's a splendid sketch artist and Rani has great journalism skills. Maria is more the average protagonist until actor Yasmin Paige's own academic life persuaded her to leave the show. Kelsey was just a pilot-only character who got a Second Episode Substitute in the form of Clyde because there were too many females in the cast... and she was a bit bratty, too. Luke and Sky don't fit this trope as they were created to be extraordinary. In fact, Luke ends up going right into college because of his high intelligence.
Hao Xuan, or so he claims, from School Shock when the school is over run with terrorists and he finds himself in a hostage situation, only to be saved by Liu Lu who's new mission (after defecting the terrorists) is to protect him as he is a "Child of Eden", something that a lot of dangerous people seem to be after.
Emma Grayson of The Elysium Project is an ordinary teenage girl who happens to be the daughter of the creator of the eponymous Elysium formula, a Super Serum which grants people reality-bending powers, and as a result ends up getting exposed to the formula and targeted by the villains.
Kyo Kusanagi in The King of Fighters, although as the series went on his high school student image was dropped entirely (it's also been implied that he never attends high school at all due to his constant fighting).
And according to the Maximum Impact series, he's spent so much time fighting and training that he still hasn't graduated from high school.
Soma Cruz from Castlevania: Aria of Sorrow. The game specifically says he is a high school student on a foreign exchange trip to Japan. The reincarnation of Dracula.
Kazama Jin from Tekken started out somewhat ordinary, but things haven't been exactly going well since. Ling Xiaoyu is a milder example. The Tekken 5 ending for Kazama Asuka suggests she might be more than just a brawler, too.
Kasugano Sakura seems like a typical schoolgirl enamored with a rough famous fighter. Aside from the fact that instead of trying to date him, she prefers mirroring his moves as best she can. Including martial-arts fireballs. Everybody in Rival Schools.
Fei from Xenogears plays almost every part of this troupe. Yeah, he knew martial arts but he thought it was just "normal" martial arts. Besides knowing martial arts that can destroy God and giant robots, he's also the only one that can pilot a special gears, which turns out to be the super ultra special one in the title. He is also secretly one of the most powerful beings in the game's universe, whom "God" gave his power to. While he is utterly oblivious to all or this at the beginning, he also has several split personalities. One of which has shut himself off from the world, and another which is an utter sociopath who makes full use of his godly power.
Makoto Naegi from Dangan Ronpa is this in a nutshell. In his intro, he keeps re-iterating how normal and unremarkable he is, almost saying the trope word-for-word. He's overtly plain compared to the rest of the cast of crazy characters.
Played with in the Nasuverse, where Shiki and Shirou know they are not ordinary, yet fail to realize the full extent of how extraordinary they are.
Takeru in ''Muv-Luv' is a typical harem protagonist who is dragged into an alternate crapsack universe
Battler, from Umineko no Naku Koro ni. All his powers to "fight" witches were granted by the witch herself, at least at first. The 'student' part of him has not much focus, though, as the story take place in his off day with him getting killed and all.
Ethan Kairos in Time Hollow is completely ordinary. He just happens to be the latest in the line of his family to receive the power to adjust history via a special pen.
The English manual quotes this trope exactly, describing him as an "ordinary high school student".
The Ultimate Luckster, Makoto Naegi of Dangan Ronpa, considered himself one, since he was picked to go to elite academy Hope's Peak by winning a lottery. His only outstanding trait is that he tends to be more optimistic than others. Not so ordinary anymore when that same optimism helps defeat the Mastermind, Junko Enoshima, the Ultimate Despair.
Hajime Hinata and Nagito Komaeda of the sequel game can also qualify, at least at first. Despite Komaeda's title being the same as Naegi's and the fact that he got into Hope's Peak under the exact same circumstances (lottery), he's stated to have legitimate, extreme fluctuations between good luck and bad luck. Hinata, however, is revealed to have no outstanding talent, and is actually an Ordinary High School Student from one of the reserve groups. At least, before his transformation...
Matt N Dusty has Matt. No magic powers, no super-intelligence, no respect from anyone.
Darkbolt: The lead three characters (Naoko, Mariko, and Yun) start out as this before being force-bonded to demons trapped in small little orbs.
Iris Kolrick and Jacob Freeman from Shadownova. Iris is later revealed to be an Esper with pyrokinesis but Jacob is truly ordinary.
Agatha Clay is an ordinary (if exceptionally clumsy) student at Transylvania U., raised by completely ordinary parents. Until it turns out her father is a famous hero, her mother is some kind of evil goddess, the most powerful man in Europa wants to imprison her (while his son would like to "form a mutual alliance" with her), and she might cause an apocalyptic disaster just by existing. She stops being "ordinary" pretty fast.
Yuri Mikagami in the round-robin story Dark Heart High. A bit of a subversion as its revealed in the very first scene that her father is a retired Evil Overlord. (A non human one at that!)
As far as Survival of the Fittest goes, it would be easier to list exceptions, since everyone in the entire cast is an Ordinary High School Student. For example, Johnathan Michaels of V2 was a world champion boxer and Renee Valenti of V3 a burgeoning movie star.
Ben 10: Ben was an Ordinary Elementary School Student, but was the star of the (apparently hugely popular for high school) soccer team at the end of the Time Skip.
Well, he was the goalie anyway.
Code Lyoko: Every member of the group is an Ordinary Student, though Jeremie is the only one who can use the Supercomputer, Aelita is the only member who can deactivate towers, and the other three are her protectors.
Aelita's status is a lot more complicated; she didn't start out ordinary in any sense.
Oddly enough, William is an actual Ordinary Student until Season 3. Debate has been going on for quite some time on several fan forums as to whether he's still a Warrior or an Ordinary Student in the series finale.
Freakazoid!s Dexter Douglas - 'Nerd computer ace, when surfing on the internet he got zapped into cyber space! He turned into the Freakazoid! He's strong and super-quick!' is an excellent example, as Dexter didn't ask for his powers, and indeed Freakazoid is an entirely separate personality from Dexters.
Doug Funnie is an Ordinary Elementary School Student in the Nick show, and Ordinary Middle School Student in the Disney one.