Vagabond

Author(s): INOUE Takehiko,YOSHIKAWA Eiji

Status(s): Ongoing

Reviews: Mature story about the most famous samurai in Japanese history. Musashi looks for salvation through his own blade. Lots of philosophy in here.

Vinland Saga

Author(s): YUKIMURA Makoto

Status(s): Ongoing

Reviews: Mature story about a viking orphan who grows up in 10th century violence. Pretty serious, great character development, definitely not shounen.

Onepunch-Man

Author(s): ONE

Status(s): Ongoing

Reviews: Not technically an adventure manga, but this is too much fun to leave out.

Nanatsu no Taizai

Author(s): SUZUKI Nakaba

Status(s): Completed

Reviews: Good take on Arthurian legend and western tropes. Characters are fun, the plot moves pretty well, too. The art may take a while to adjust to.

Flow

Author(s): Honey Bee

Status(s): Completed

Reviews: Great setting with spirit/soul animals that grant one wish to their human. Gets a bit dark, but it's a really interesting story. Moves quickly.

UQ Holder!

Author(s): AKAMATSU Ken

Status(s): Ongoing

Reviews: Technically a sequel to Negima, but I haven't read that and I'm still enjoying UQ Holder a lot. Really fun, moves pretty well too. Harem.

Ruler of the Land

Author(s): JEON Geuk-jin

Status(s): Ongoing

Reviews: Pretty ridiculous historical fantasy. Lots of fun, moves really fast, so you're never bored. Plot takes a while to develop, but it gets really good.

Boku no Hero Academia

Author(s): Horikoshi Kouhei

Status(s): Completed

Reviews: Pretty fun so far. The plot seems a bit thin, but it's a great setting. Hero school.

Letter Bee

Author(s): Asada Hiroyuki

Status(s): Completed

Reviews: Great imagery. A boy decides to become a deliveryman in a dangerous world. With only an artificial sun above the capital, it gets dark in the wild.

Desert Punk

Author(s): USUNE Masatoshi

Status(s): Ongoing

Reviews: A gun for hire in the desert. Lies, cheats, and steals his way to fortune. Pretty funny.