I sort of liked it. It's amusing and it has amazing action sequences. It was a massive explosive mega-hit with lots of anime fans, but personally I struggled a bit when trying to watch back-to-back episodes. At root it's a one-joke show and I'm not sure it supports too much consecutive watching of that joke.
The title character is Saitama, whose name isn't One Punch Man but might as well be. He's probably the strongest superhero in existence. He's the ultimate culmination of all those "I HAVE TO GET STRONGER!!!!" shounen heroes... and this has ruined being a superhero for him, because his fights all last one punch. No one in the world stands a chance against Saitama. In fact, everyone in the entire world attacking en masse probably still wouldn't stand a chance against Saitama. When he really lets rip, just the shockwave from his punches could pulverise a mountain on another continent.
Saitama is thus bored. He's also a deadpan ordinary bloke who underreacts to everything in a world of superheroes. This is funny. He talks to megalomaniac supervillains as if they're the checkout girl at the local supermarket. He'll usually be popping out to buy a beer, doing the ironing, buying a takeaway because he can't be bothered to cook and so on.
This is pretty good satire. It's taking the mickey both out of recognisable Western superheroes and their manga-specific tropes. However the downside of this is that the show isn't even trying to create dramatic tension, except in a slice-of-life way. Saitama's abilities aren't being acknowledged by the superhero association, for instance, and he'll be classified as C-grade because he flunked the written exam. (The superhero association is stupid.) Villains, though, are cannon fodder. They'll show up. They'll brag. They'll often be genuinely impressive and cause so much devastation that even Superman would start worrying. However we know it's all going to be resolved in one punch, with everything beforehand being embroidery.
It's also cynical. This is for comedy, obviously, but even so this is a world where no one cares much about massive loss of life and heroes are liable to get blamed for the destruction caused by villains. They were fighting them! Fights cause destruction! Case closed! The public are jerks. There's also a superhero ranking system that causes all kinds of snobbery, jealousy and patronising assumptions. Even Saitama himself doesn't take heroism seriously and says he's only doing it for amusement.
Fortunately the show has so much style that it's still entertaining despite all this, but it helps to be watching episode by episode. Nothing really matters. I understand the manga later spreads its focus beyond just Saitama and gets a bit more serious, but what I've seen so far of the anime hasn't got there yet.
The animation is special, though. It was the standout show of 2015 and it blew away everyone in the industry. The director actually had to release a statement saying that they only had an ordinary TV budget. It's basically anime with the brakes off, with the action sequences given licence to do whatever they really want to do. It's still anime, mind you. It usually looks conventional. You'll acclimatise. Your brain decides that that's the new normal, or perhaps viewers who aren't animation nerds might not have noticed anything different in the first place.
Even the character designs are interesting. The original source material is a web comic that looks as if it was drawn by a five-year-old. This was adapted into a more conventional manga by Yusuke Murata, who's very good. We thus have an unusual mix of styles, with Saitama normally being drawn as if the artist was bored. (This suits his personality.) However he'll acquire a more dramatic look when something riles him. This is the opposite of what happens with Tatsumaki and her highly distracting skirt, since her anger-induced art shift is into web comic mode, not from it.
This is quite a good show that got lots of attention and I believe it's getting a second season. However I don't think I'd be interested in more of the same. It's explosively dynamic and I like its basic joke, but a long-running series can't survive on that joke alone. I want more attention given to the supporting cast, who can't win every fight in one punch and hence can create dramatic tension. Some of them are good, after all. Saitama's self-appointed disciple Genos is amusing in his humourless way. Tatsumaki made me laugh in ep.10 when telling the Dinosaur King that she was on the phone. Silver Fang is cool. Puri-Puri Prisoner has drawn polarised reactions, though. I'll definitely be checking out Season 2, but with a modest amount of caution.