Saiki Kusuo no Psi-nan (Otherwise known as The Disastrous Life of Saiki K.) is a comedic gem, hidden from the eyes of many comedy anime fans. I'll focus this review on both S1 and S2, but TL;DR: Watch Saiki K.

Story:

It's difficult to rate the story for Saiki K as, well, it doesn't really have one. The main premise is that Kusuo Saiki is a high school kid with an absurd amount of superpowers who just wants to live normally and peacefully, but has so many annoying friends and family members that prevent him from doing so. The comedy throughout the series is fast paced, and always spot on. There wasn't a single scene which I didn't find funny in the whole two seasons I watched (twice).
If we're trying to rate the story, I'll have to give it an 8/10 because, although it's simple, it's super effective and brilliant.

Characters:

This is where Saiki K shines. Every character is just a trope, but they're so well done and over the top that they're never boring to watch. You have Saiki - the stupidly overpowered main character, Nendou - the super dumb kid, Kaidou - the chuunibyo, Teruhashi - the "perfect girl", Mera - the glutton, Yumehara - the hopeless romantic, and so on.
Not only that, the character progression is also brilliant. The development of Saiki's personality towards his "friends" is incredibly interesting. The more of Saiki K you watch, the better it gets.
The characters also result in great humour, whether it be Saiki's trademark bored voice (also seen in Koyomi Araragi from Monogatari and Levi from Attack on Titan) or Teruhashi's attempts to make Saiki notice her. They're just so entertaining.
My rating for characters is obviously going to be 10/10.

Art and Animation:

Fairly cheap, but bright and fitting. Not really much else to say about that. The anime doesn't really need good animation, but the art is honestly fine for this. Nothing bad enough to ruin the anime, nothing good enough to make it stand out. J.C. Staff did okay with this.
I'll rate this 9/10 because there isn't really much to say.

Music:

Again, nothing about the music stood out. It was always fitting to the mood and sounded good. The opening and ending songs were also always fitting (especially OP and ED 4; they were both amazing).
I'll rate this 9/10 as well because again, there isn't really much to say.

Enjoyment:

The enjoyment I had from watching this was off the charts. So many scenes had me in tears, and every time I watched one episode I didn't want to wait to watch the next. Not many other anime have made me as happy as I did watching Saiki K, and honestly I don't regret watching this one bit.
My enjoyment will of course be 10/10.

Overall:

Saiki K will always be one of my favourite comedy anime. It was just so funny and amazing, and I don't know where I'll see something of that level again. Overall, it's 9.2/10, but the reasons it isn't 10/10 are so small that they don't really affect anything.
And again, watch Saiki Kusuo no Psi-nan.