It's a gag anime. Almost no plot lasts more than an episode and nothing permanent ever happens. I wouldn't call it marathonable, but I quite enjoyed it and it's good for a laugh.
Saiki Kusuo is a psychic with superpowers. Which ones? Well, all of them. He can basically do anything, although his powers often have some kind of arbitrary limit for the sake of storytelling. There might be a cooldown period before he can use that power again, for instance. These powers include:
1. TELEPORTATION, to anywhere in the world, or indeed into outer space (where he's fine with hard vacuum). He can't time travel, but he can...
2. REVERSE TIME, on anyone or anything. This will heal any damage, including death. (...I think. I'm not completely sure on that last one.)
3. SHAPESHIFTING. He can turn into an animal, a girl, etc.
4. X-RAY VISION (involuntary). He's thus completely uninterested in seeing naked girls, partly because his X-ray vision goes through skin to the muscles and bones underneath.
5. TELEPATHY (involuntary). He finds other people annoying, except for the one person he can't read (Nendou the idiot), who he finds annoying for a completely different reason (i.e. he's Nendou).
6. SUPER-STRENGTH, SUPER-SPEED, etc. He has trouble not breaking things and always tries to place exactly halfway in all races and competitions.
7. CAN TURN INVISIBLE
8. REALITY CONTROL, which is used in ep.2 to deconstruct anime/manga cliches and explain why people in Saiki's world have unnatural hair colours, can heal light injuries immediately if they were funny, etc. Saiki rewrote the laws of physics.
9. PETRIFICATION GAZE (involuntary), which is why he wears those glasses. Don't take them off.
You get the idea. Saiki has to wear two Christmas tree decorations on his head. They're power limiters. If he ever loses those, he'll destroy anything he touches and cause a hurricane if he so much as moves. He can't visit the cinema because spoilers get beamed into his head, whether he likes it or not. Unsurprisingly, Saiki's become a profoundly negative person. He thinks everyone's an idiot (which is fair) and he's completely unmoved by almost everything. Girls are annoying. Friends are annoying. He just wants to eat desserts (especially coffee jelly) and not be noticed. His reaction to everything is an acidic deadpan as he tries to escape from all these morons who think they're his friends. This could have made him a deeply unpleasant character, but fortunately he's also quite likely to end up helping them out of trouble. He'll just be doing it for cynical reasons, e.g. it would be annoying to owe them a debt, or he wants to get home and play a bad computer game.
This is quite funny. Cute girls (Kokomi Teruhashi) and adorable pussy cats (Anpu) will suffer brain overloads because they can't process someone not going gaga over them. Saiki's jaundiced attitude to romance is one of the show's more original aspects, as are the lengths he'll go to to avoid girls who fancy him. (It's hardly surprising, though. We look like zombies to him and he can hear your every stupid thought.)
That's half the show. The other half is, of course, the supporting cast. These are... only okay, actually. Nendou's an idiot, supposedly, but most of the time he's just a big, amiable guy with a testicle-shaped chin. Kaidou's a chuunibyou who thinks he has Saiki's powers. Hairo's hot-blooded. Toritsuka's a mildly perverted psychic who can see the dead. It goes on. The show develops quite a big cast, but it doesn't have any laugh-out-loud hilarious supporting characters. No one stands out, although the girls fare better than the boys. Teruhashi is quite an original (and funny) character type, Chiyo Yumehara can be a parody of all kinds of girly manga tropes and Mera Chisato is a dirt poor student with lots of younger siblings, several part-time jobs and an opportunistic attitude to food.
It's funny, but it's not "roll-on-the-floor guffaw" funny. It's a rental, not a purchase. It took me a while to get into it, I think, so I found the second half funnier than the first half. I laughed aloud a few times, but this was generally at something fleeting like a particularly good one-liner. There's certainly no tension or drama. Saiki can basically do anything, so his actions will usually be driven by nothing more weighty than his love of desserts and/or his desire to avoid people who annoy him (i.e. everyone). One of the show's stronger areas is comedy observation, in fact, so I liked its analysis of, say, bad computer games, manga cliches and Tsundere Grandad. (Unlike most tsundere characters, he's painfully easy to imagine existing in real life.) It also impressed me in ep.21 by visiting London and showing specific knowledge of that city. (Tube strikes, Boris bikes, etc.)
It's an easy watch. Give it a go if you're looking for 25 minutes of relaxing cynicism that's likely to be somewhat amusing. By the time I finished the show, I'd become moderately fond of it.