Super Hero concepts (of the spandex/costumed kind) are rare in manga/anime but they're there. 8D Others have mentioned OnePunch-man and Tiger&Bunny. There's also Ratman (which is not as popular as the first two, btw OnePunch-man is awesome!). There are more which I haven't read/watched, like Zetman and My Hero Academia but I think they fall under the superhero genre.
I didn't read Marvel/DC comics when I was a kid, but what I've seen on tv (like the animated series and movies) intrigued me. But thanks to the many superhero movies that are popping up in cinemas since the early 2000s (my word, I feel old) now I'm more open to the genre than I was growing up.
Heheh, also... I saw the word Super Hero and I can't help but do a bit of self-promo XD;;;; My comic The Masked Henchman is set in a superhero setting but it's more slice-of-life than action and more in the views of a bystander than an actual hero. (It's also heavily influenced by OnePunch-man. XD;;;;;)