Abandoned Warehouse District: There's an entire region of town which, for some reason, the monsters always attack; so, unsurprisingly, nobody lives there anymore. It's Saitama's neighborhood, and it's implied that powerful monsters attack there so often specifically because they've heard how strong he is and want to fight him. To the point that an entire monster organisation has made their base there.
The Ace: Genos is patient, intelligent, self-sacrificing, and a terrifyingly skilled fighter with a strong sense of justice. All this means he's pretty much playing the eternal Straight Man to Saitama's lackadaisical approach to heroism, although ultimately Saitama is still far stronger.
Art Shift: In Murata's version, Saitama is usually drawn incredibly half-assed, in stark contrast to the ridiculous level of detail given to almost every other character and background, reflecting his attitude toward everything. Whenever he starts taking things seriously and acts like a badass though, he's drawn in the detailed style. Tornado seems to adopt this tendency of normally being poorly-drawn herself when she's angry/pouting.
Badass Moustache: The hero Spring Mustache is apparently named after his, admittedly very stylish, mustache. Bang also has an awesome old man-style mustache.
Badass Normal: In the second issue, we get a flashback to the time before Saitama gained his incredible strength, when he fought a crab monster with nothing but normal human speed, strength, agility, and a necktie. He won.
Empowered Badass Normal: There are strong hints that while Saitama thinks he got his power (and lost his hair) due to simple training, some unknown factor might have empowered him. He suffered strange pains when his training routine started to give him powers, implying some sort of transformation, and the end result were powers he imagined that superheroes have. We also have an example of a minor villain who turned into a superpowered "mysterious being" (albeit far weaker than Saitama) simply by shadow-boxing a lot.
Blessed with Suck/Cursed with Awesome/No Challenge Equals No Satisfaction: Saitama is able to defeat any foe with a single punch... which means that to him, his battles with evildoers are about as exciting as a trip to the grocery store to pick up a gallon of milk. Even so... he can defeat ANYTHING with a single punch, up to and including 100 foot tall giant monsters. Effortlessly.
Except Boros and Garou, who could take some punches. In Garou's case, he actually survived after losing to Saitama. They're still no challenge to him; he's only shown a couple moves from his lethal "Serious Series", and Boros complains (as he lays dying) that Saitama was still holding back.
Blood Knight: Saitama. He first became a hero when he rescued a child from a monster after being fired from his previous job with no hope of getting a new one. He felt such a rush after this first heroic rescue that he dedicated himself to becoming a hero. At one point he has a dream about being attacked by an army of monsters that actually CAN give him a challenge. The next morning, he goes up against enemies similar to those in his dream, but not as strong: he's left horribly disappointed.
Saitama sometimes pulls out the "Normal Chain Punch". On the rare occasion that he gets somewhat serious, he also has a lethal "Serious Series" of power moves.
Silver Fang teaches the "Water Stream Rock Smashing Fist" to the students at his dojo. His brother is master of the "Whirlwind Iron Cutting Fist". The techniques can be combined into the "Cross Fang Dragon Slayer Fist". After learning these and a dozen other "fists", Garou creates the "Monster Calamity God Slayer Fist".
Even Licenseless Rider has moves like "Justice Crash" and "Justice Tackle".
Charles Atlas Super Power: As far as we know, Saitama has no magic or mystical superpowers, just an incredibly strong and well trained body; yet his training has made him as strong as Superman, with no weaknesses.
The training wasn't even that outlandish: 100 sit-ups, 100 squats and running 10 km every day. Strenuous, sure, but barely Olympic-level strenuous.
It seems to be almost a law of physics in the setting; several monsters indicated that they gained their powers and transformations by doing one thing obsessively, such as eating huge amounts of crab and turning into a crab monster.
Chekhov's Gunman: The boy who Saitama saved in his Origin Story has a grandfather who's a multimillionaire and thus founded the National Superhero Registry. The grandfather founded it exactly three years ago after hearing how Saitama saved his grandchild.
Also, the House of Evolution. After the arc with them as the Big Bad, they completely disappear from the story. Until many chapters later, where it is revealed that Zombieman, the eighth ranked S class hero, was one of their creations.
Clothing Damage: In Chapter 6, Saitama has all his clothes blown off by the blast from one of Genos' attacks.
Comically Invincible Hero: Although during the comic's few more contemplative moments, he's also a Tragically Invincible Hero.
Continuity Nod: Chapter 20 has the Hero's Organization investigating Saitama's neighborhood and finding all the damage from his previous fights, with the destruction caused by the giant in the B and D cities also mentioned.
Stinger did not even get a chance to fight back against the Sea Folk's king.
Garou gave one to the S-Class Heroes after becoming a Mysterious Being. Until Saitama appears, that is.
Cut Lex Luthor a Check / Mundane Utility: After being defeated, the head of the House of Evolution uses his talents at creating regenerating bodies to produce unlimited octopus tentacles... and opens up a takoyaki stand.
Determinator: The main reason Saitama has become so strong is due to his ability to stick to his hellish workout schedule for three years in a row.
A later flashback chapter shows this may have always been the case as far back as age 12, where he kept chasing a man-sized mysterious being that stole his money from two bullies that were shaking him down until it knocked him out.
Disproportionate Retribution: Lampshaded when Saitama calls out a crab monster for trying to kill a little boy who drew nipples on its shell with permanent marker.
Dissonant Serenity: Saitama usually approaches his fights with a completely impassive, almost bored expression.
Event Flag: Lampshaded in the fight with Garou, when Saitama, who had been excited at the prospect of finally getting a decent fight, starts to get angry when Garou keeps hitting obvious "loser flags" with his hokey villain monologue.
Facial Markings: Sonic has red stripes under his eyes. Tank Top Tiger has tigerish markings.
Fearless Fool: Class C Rank 1 hero Licenseless Rider has tried to face down a horde of power-armored terrorists and a nigh-invincible monster that defeated multiple S-class heroes, despite having no apparent superpowers of his own (one of his named attacks is throwing his bike at them). He barely survives both encounters, but he's also one of the few people who realizes Saitama actually defeated the Sea King on his own.
Fish People: Ones calling themselves Sea Folk invade from the sea in Chapter 23. They're tough and numerous enough to warrant a full scale hero counter-attack.
A Friend in Need: Despite complaining about the way Genos follows him around, Saitama shows concern for him and even fights Asura Rhino on his behalf when he gets turned into "modern art".
From Nobody to Nightmare: Garou, who goes from a nobody to becoming one of strongest being on the series capable of fighting against several S class heroes and defeating them. He's also the second person in the series to survive Saitama's punch... for all the good it does him.
Saitama is an example of this himself. Going from a melancholic out of work Salaryman to a nigh unstoppable force of nature any supervillian or monster who knew what was good for them would be existentially terrified of.
Beefcake rips out of his clothes when he grows to giant size and goes on a rampage.
Saitama: Put on some pants, will ya?
Saitama himself also ends up defeating Mosquito Girl naked after Genos accidentally incinerates his clothes.
Funny Background Event: When our heroes must climb a mountain to get to the House Of Evolution headquarters, we see the path they took and a sign saying 'Beware of the Bears'... with an unconscious, bloodied bear lying right beside it.
One random panel in Chapter 19 has a crow with human arms and legs stealing a fishbone from a cat.
The hellish training aspect is played for laughs. 100 push-ups, squats, and sit-ups are barely afterthoughts to professional athletes (and they typically don't punch out skyscraper sized monsters). Running 10 kilometers every day is more difficult, but certainly not insurmountable depending on the pace.
Gonk: Any of the family gifted with unfortunately large cleft chins.
Gorn: The titular One Punch can make your skull explode. The one time so far that Saitama uses a multi-hit combo (called Proper Chain Punch), it liquefies every part of his opponent above the waist.
The Greatest Story Never Told: Saitama eventually realized he isn't famous even though he's been saving the city as a hobby for quite some time. Turns out, he needed to be registered as a superhero to get credit. If you don't, the general public considers a "hero" as just a weirdo in tights.
Groin Attack: Saitama does this (accidentally) to a ninja. The ninja survives, though Saitama held back.
Hard Work Hardly Works: Completely subverted with Saitama's training schedule. It's a brutal training schedule that is of the "Kill You Or Make You Stronger" variety. And said schedule has made him stronger than any other character out there. When he registers to become a full-fledged hero, while he did poorly on the written test, in the physical portion, he set records in every category. It has been hinted that, in addition to whatever Saitama did, something else contributed to his becoming so incredibly powerful, something Saitama himself does not know of.
Heroic BSOD: Saitama has a brief one when he realizes he's become too strong and can't enjoy fighting any more. Luckily Genos then turns up to make things interesting. Then he has another one when he realizes he's not famous.
Hero Killer: Garou, one of Bang's former but still BEST student.
He Is A Monster: Pretty much everyone's reaction to seeing how strong Saitama is.
Hollywood Cyborg: Genos; it's currently unknown how much, if any, of his body is still organic.
Kaiju: Gargantuan humans, bugs, and sea creatures.
Loads and Loads of Characters: New characters have been introduced at a steady pace, but starting with the sea monster invasion arc over a dozen new A and S-rank heroes are introduced. Some awesome, some crazy, some Crazy Awesome.
Me's a Crowd: The scientist who founded the House Of Evolution made numerous clones of himself to assist with research. They get turned into a Red Shirt Army.
Mistaken for Gay: When Saitama is informed that a scientist has "taken a great interest in your body" (for experiments), he replies that he doesn't swing that way. Genos corrects him.
Mook Horror Show: Asura Rhino can sense how powerful Saitama is. This is how he looks to someone who can sense how powerful he is. All the more terrifying because Asura Rhino is indicated to be the most powerful being encountered so far (stronger than even the hundred foot giant from an earlier issue), and has never feared anything in his life, but in seconds, he goes from being a Smug Super to screaming in fear and immediately breaking off his attack.
All my instincts are screaming at me... Get away from him! He's dangerous!
Monstrosity Equals Weakness: Saitama claims that Garou's has never been weaker after he changes into an even bigger mysterious being while trying to beat him, As opposed to the smaller more human monster he was before.
Saitama can defeat anybody with a single punch. This means that should he deign to pull out such simple moves as a combo that anybody can master (The Normal Chain Punch, for example), better start praying for his opponent.
An entire faction of heroes, reaching all the way to S-Class, is dedicated to Tank Tops.
Also Boros, leader of a group of space raiders. Saitama, however, finds the idea of rampaging across space just because you're bored moronic.
Non-Powered Costumed Hero: Many of the lower-class registered heroes seem to have no superhuman powers at all, Licenseless Rider being the most obvious example (although his powers may have been overshadowed by the supervillains he faced).
Asura Rhino, the most powerful being encountered so far, is the first villain to be able to accurately gauge Saitama's power. Before doing so, he was supremely confident in his invincibility, but then his survival instinct kicks in.
Also, anything rated threat level Demon tends to cause a Mass "Oh, Crap!" for everyone in the city.
The previously smug superhero candidates suffer a collective one when they realise just how powerful Saitama is.
Person of Mass Destruction: Any individual rated threat level Demon or above qualifies for this; Demon-level threats threaten an entire city, Dragon-level threats threaten multiple cities, and God-level threats threaten all of mankind.
Petting Zoo People: The members of House Of Evolution are all these, including a mosquito, a lion, a slug, a frog, a mole, and a cyborg gorilla.
Power at a Price: Played with; when he reappears later on, the head of the house of evolution says that Saitama's power came at a great price... he became bald. Immediately afterwards, though, he plays it straight, indicating that as he sees it the real price of Saitama's power is the way it has alienated him from the rest of humanity.
Going bald as the price for power (and having it treated as if it is a serious, terrible price to pay) is a Running Gag throughout the comic.
Punch Clock Hero: Saitama mentions that he doesn't really believe his heroics will have much of an effect upon the world and he only does them because they bring him excitement; or at least they used to.
Pursue the Dream Job: Saitama quit being a run-of-the-mill salaryman and trained for three years so he could take up superheroism as a hobby.
Several to Anpanman: in Japanese the titles are similar (Onepanman/Wanpanman), Saitama's costume is based on Anpanman's, and the name of the series' first villain, Vaccine Man, riffs on Baikinman ("Germ Man"), Anpanman's main villain.
The cover page to chapter 3 features a suspiciously Godzilla-like kaiju.
Genos's backstory is similar to several Kamen Riders, especially those of the Showa Era. There's also the Licenseless Rider, who rides a bicycle to battle. His hero name in Japanese - Mumen Rider - is another pun on Kamen Riders.
Slasher Smile: Sonic is often sporting one, which he refers to as a bad habit.
You just want to try your techniques on me. I can tell by that child-like smile on your face.
The Social Darwinist: The House Of Evolution was made for the purpose of evolving humans beyond their current limits, since the genius creator found everyone he met to be inferior to him. He gives up when he meets Saitama, an ordinary man who surpassed his limits with sheer determination alone.
Done deliberately in group artwork, where Saitama is often pushed to the side and cooler-looking characters like Genos are made the most immediately noticeable.
A good example is the Volume 2 cover◊, which consists of Genos looking good in the foreground and Saitama crammed into the corner, looking stupid.
Stylistic Suck: The crude art of the original webcomic is deliberate. ONE can draw very well when he wants to.
In both the webcomic and the manga, Saitama in particular is generally drawn in a much more simplistic, lower-quality style than everyone else.
Super Registration Act: The National Superhero Registry. Only registered members receive fame and fortune for what they do; those that don't sign up are pretty much just costumed lunatics in the public eye.
Teach Me How To Fight: The already ridiculously strong cyborg Genos starts following Saitama around calling him 'sensei' and asking to become stronger. When Saitama tells him how he achieved his current strength, however, Genos is kinda disappointed.
Training from Hell: Parodied. Saitama does 100 push-ups, 100 sit-ups, 100 squats, and 10 kilometers of running every single day with no breaks. Said training was what caused him to go completely bald. Note: This doesn't even begin to approach the level special forces soldiers or professional athletes train at.
A Twinkle in the Sky: Mosquito Girl is slapped aside by Saitama and dies from it, most likely because she was knocked through at least one building in the process.
Ungrateful Bastard: Despite Saitama's heroic efforts of destroying the gigantic meteor and dividing it into smaller pieces just so the city would still be intact, a lot of the Z-City citizens are pissed thanks to him destroying the giant meteor in the first place. He does however counter with his very own awesome "World of Cardboard" Speech.
Unlikely Hero: Though the decision to become a hero was Saitama's own, his main motivation seems to be boredom and he often gets frustrated by the ridiculous situations he finds himself in. Consider how most heroes start their stories. Most of them were for revenge or to get acceptance.
Up to Eleven: Saitama's strength training is absurdly simplistic and played for laughs, but it prepared him to defeat skyscraper-sized monsters with less effort then Superman does...somehow. The other characters who have heard his explanation comment on how flat-out impossible his strength is when compared to what he claims to have done.
Not simply his strength, but his speed is so far beyond super-human it is ridiculous. During the first confrontation with "Speed of Sound" Sonic, Sonic spends half a chapter trying to intimidate Saitama by ricocheting randomly off the trees around him at super speed. When Sonic asks if he can even see him, Saitama instantly turns his head towards him (with a disturbingly motion-blurred face) to ask if he can go home now.
Equally Saitama is lazy beyond anything seen in a shonen, to the point where half the time the artist can't even be bothered with shading him in.
Wall of Text: Genos' backstory is delivered this way as a joke. Ever wonder what an origin story sounds like without a flashback? Now you know.
We get another one explaining the National Superhero Registry, presumably also provided by Genos for Saitama's benefit.
What Measure Is a Non-Human?: Saitama never hesitates to kill monsters—even one that was running away—regardless of intelligence, yet he lets human criminals live, including a guy who killed a whole building full of people for no reason.
This later becomes a major element of the Garou plot arc, as he's a human who thinks it's unfair that the heroes always win and the monsters always lose. He ends up following the trope to a T anyway, which is why both the monsters and Saitama refuse to consider him an actual monster.
Genos has yet to win a good, honest, major fight, despite his S class status. The one fight he did win was all off-screen.
Virtually every hero and villain gets Worfed. A is beat by B, who is beat by C, etc etc in a continually escalating battle of badassitude. And whoever is the mightiest gets to be one-punched.
World of Badass: Superheroes are incredibly common here, so much so that no one acts surprised when insanely strong guys in silly costumes turn up day after day to battle the forces of evil. This might be subverted though; while there are a lot of 'heroes' in this country, most of them are not at 'heroic' level. C to B class heroes on average class handle threats that most soldiers/policemen can handle. Most of the threats that currently come into the world are usually impossible to handle unless it's by an A class or S class hero and even they are sometimes not enough.