In anime, the typical protagonist starts off as a small fry who wants to attain great things. He finds a wise, old teacher that guides him part of the way but then a major threat appears. In One Punch Man, our protagonist is already at the peak of the power curve and can actually one-punch-kill anything. His nemesis is — boredom.
Saitama decided to become a hero because he thought it would be fun but it turned out as anything but. He can kill anything in one punch, though he most often holds himself back and regrets ending fights too soon. He has heard every antagonist rant there is, has seen all the flashy transformations and power-up metamorphoses there are and is totally nonplussed as the world around him gets incinerated and he is tossed around like a ragdoll.
We get to see Saitama's power in the very first episode, where he is confronted with Vaccine Man, who wants to punish humanity for spreading their filth. As the name of the anime implies, one punch and Vaccine Man is history (click the image for a 1920x1080px, 202 KB version).
For some reason, I identified with Saitama right away. It is actually true that being too good at something can make you feel like there's no reason to continue doing it. The best part is, nobody's giving him any credit for basically punching out gods and saving the entire city. Fangirls swoon over generic pretty-boy heroes who do nothing while Saitama actually gets booed and shunned in the public for what people see as being a weirdo.
Saitama soon meets a cyborg, Genos, out for revenge against another cyborg that leveled his village. That revenge plot is quickly forgotten since Genos gets floored by Saitama's power and asks to be his student. Saitama doesn't see the appeal but allows him to tag along. What later happens is that Saitama does all the work but nobody believes it and Genos gets all the glory.
Genos begs Saitama to join the Hero Association with him and get the credit he deserves. He agrees and they hope to rub elbows with the most powerful heroes in the country. Soon after, Genos asks Saitama for a sparring session. They fight in an abandoned quarry and Saitama holds back until Genos asks for a real challenge, "without mercy". What Saitama does is outmaneuver Genos to appear behind him, ready to strike (click the image for a 1920x1080px, 164 KB version).
Here we get a moment of brilliance and the perspective of Saitama's victims before they're pulverized. At the last moment, Saitama pulls back and Genos realizes he was about to get atomized in a single punch (click the image for a 1920x1080px, 131 KB version).
When he takes the Hero Association entry exam, Saitama dominates the physical test, crushing the test machines but fails the written essay, which means he lands in the 4th tier of heroes. To illustrate the kind of heroes in that tier, one of them is called Mumen Rider and his special move is that he throws his bike at the opponent. It's not super-powered or anything, he literally just picks up the bike, calls out the attack and throws it at the truck-sized monster that can knock down buildings in one swoop. His other special move is Stand-Up Pedaling.
I found this brilliant, since I was always wary of the way schools make brilliant students think they're failures by averaging their grades. To put it bluntly, Nikola Tesla might ace his math and physics exams but fail push-ups, netting him an average total grade even though he's a world-changing genius. Anyway, Saitama later on gets accused of having cheated on the physical exam and nobody believes he has any power, with some even accusing him of being a tag-along that kills the weakened monster after the strongest heroes have fallen, which does actually happen.
Top-tier heroes turn out to be whiny, conceited bastards, without a shred of integrity or humility. They play mind games all the time and vie for status and glory rather than try to help the common folk, who are besieged by all kinds of villains and monsters. They do come together in the season one finale, however, but the low-tier heroes, the kind of Mumen Rider, are the ones who show true heart, teamwork and self-sacrifice.
Season one finale has the villain deliver a backstory that seems similar to Saitama's: he's so powerful and bored that he searched the galaxy for a worthy challenge. One thing did irk me here — Boros says he was searching for 20 years, but the concept of years doesn't exist beyond Earth. Anyway, Saitama lightly punches him, shattering Boros' armor and causing him to power up to his advanced form. As Boros does so, Saitama is nonplussed (click the image for a 1920x1080px, 126 KB version).
In that seizure-inducing fight, Saitama actually has to use one of his Serious Punches rather than just light taps. There's nothing special about Saitama's punches at all, they're as plain as boxing crosses and uppercuts. I was and still am impressed by that fight and I think you'll be as well.
Second season does introduce a whole host of side characters and a (sigh) martial arts tournament B-plot but I guess those two are staples of traditional anime, even in a show that tries to parody filler content. There are again moments of brilliance in the season two finale, which I won't spoil. Afterwards, I read the show had a different director for its second season, which seems apparent in retrospect. I didn't think much of the drop in the animation quality, finding it suitable for a show that pokes fun at itself. What now feels like a dead giveaway was the introduction of a proto-nemesis, Garou.
He's shoehorned into the show and given Saitama-level powers in terms of endurance and regeneration. Honestly, he is so one-sided and bland that I couldn't force myself to suffer through his backstory but I did figure out he wants to be known as a hero-killer. That's it, there's no twist or anything, he just hates heroes. Saitama defeats him by accident a few times, with Garou conveniently getting an amnesia every time. Nothing gets resolved between them in season two and there's no announcement of season three. Pathetic.
Season two does redeem itself with a few moments near the end. Before that, we get to see clever callbacks to earlier episodes, in particular that sparring match between Saitama and Genos. In one instance, Genos takes on an emo Naruto wannabe and tries one interesting move we saw before (click the image for a 1920x1080px, 127 KB version).
It doesn't give Genos the lethal force Saitama has but it does work to an extent. By the way, I found the angle of a young, ambitious man trying to decipher the secret to an expert's power really interesting. At one point, Saitama says some trite line and Genos actually writes it down. That's how religions got started, kids.
If you like deconstructive parody, you'll adore One Punch Man. He lets god-tier enemies go on rants and babble on about their motivations while powering up to their ultimate form before atomizing them with a single punch. All the while, he has an expression of utter boredom on his face and doesn't even flinch when being assaulted.
By the way, Saitama does punch out a meteor. How he does it and what happens later, that's for you to find out by watching the show. As for the secret to his power, it's 100 push-ups, 100 sit-ups, 100 squats and 10 kilometers running, every day.