Marvel used to have some of those genres in the 70s and 80s:
pirates:
space marines: Alien Legion (under Epic)
sword and sorcery: Conan
'50s weird horror: reprints in 70s horror mags
'60s kitsch super-spy stuff: Secret Warriors is spy stuff, S.H.I.E.L.D. is more occult than spy and occurs in the 50s

and since we're in the Masterworks forum,
we're in the middle of the 60s run of Nick Fury

and of course Marvel has had kung fu with Iron Fist and Shang Chi
Iron Fist is in New Avengers and Shang in Secret Avengers

I feel for DC who's got nothing outside of superheroes. Even Marvel's superheroes straddle other genres and allow Marvel to tell non superhero stories such as high fantasy stories for Thor, techno-thrillers for Iron Man, war stories for Captain America and even Miller, Bendis and Brubaker have told crime stories with Daredevil. And the FF are science-fiction/adventurers. Currently Namor is a fantasy title.