Action/adventure
Tower of God (manhwa, color, webcomic, adventure, fighting) The story is about a boy who gets separated from his friend, who decides to climb the "tower" for the ultimate reward. He chases her and stuff happens. Highly recommended.
Threads of Time (manhwa, adventure, fighting, historical)
A teen starts dreaming about his past life as a warrior.
Cage of Eden (action, adventure, mystery) A group gets stranded on a survival island, and they have to deal with all the dangers and uncover the mystery of the island. A real page-turner.
Elfen Lied (action, psychological, romance) Cute girl with a personality disorder. Don't remember too much about it but from what I recall it was really good.
Pandora Hearts (adventure, fighting, comedy) I'll be honest. First time I read this I had no idea what was going on. I started liking it at the second read and loving it on the third. It's about crazy people doing missions for an agency ran by lunatics. It has a good plot, and is known for having plot twists everywhere. Regardless of that, I love the characters and the story, and it's something I'd recommend.
Crepuscule (Yamchi) (action, fantasy, manhwa, school life)
Vampire manhwa about a human going to a monster school.
A Fairytale for the Demon Lord (action, adventure, manhwa, fantasy) A story about a nameless knight searching for his princess.
Shut Hell (action, adventure, historical) The mongol prince Yuhei is a pacifist who wants to preserve history. Only problem is at he's traveling with a famous killer.
Billy Bat (drama, historical, mystery) A comic artist discovers an ancient secret. Highly recommended.
Onani Master Kurosawa (psychological, drama, school life) This story is about a guy who masturbates on a school toilet. No, this is not a comedy manga.
Monster (drama, mystery, psychological) A doctor saves a little boy who's actually an evil killer. He decides to hunt him down. Highly recommended.
Jisatsutou (drama, psychological, adventure) The government decides to send suicidal patients to an island because they cost too much to treat.
Glaucos (action, sports) A young teen starts competative diving.
Kiseijuu (action, fighting, school life) A student gets infected by a highly intelligent parasite alien. Now he has to compete with the other infected humans.
Comedy
Martial Arts Extreme Hell Private High School (comedy, manhwa, martial arts, action) Silly martial arts parody with stupid humor. I love it.
Choku (comedy, romance, school life) Girl with nosebleed issues. Again pretty silly humor.
Sayonara Zetsubou-Sensei (comedy, school life) A comedy around a suicidal teacher.
It's Not My Fault That I'm Unpopular (comedy, school life) A story about a girl with no social skills who over-analyzes and misinterperets everything. It's hilarious.
Slice of life/comedy
Hell's kitchen (comedy, action, cooking) A demon appears and turns a boy into a chef. Almost certainly inspired by majin tantei nougami neuro.
Legend of Koizumi (comedy, action, gambling) Satirical manga about a japanese prime minister. It gets blown out of proportion so hard with exaggerated historical figures. Highly recommended.
Addicted to Curry (comedy, action, cooking) Guy takes over restaurant and fights other chefs.
Gamble Fish (action, ecchi, gambling) Story about a guy looking for his father, a legendary gambler. Lots of suspense in this one.
Hammer Session! (comedy, action, school life) An escaped prizoner and swindler starts teaching at a school, where he helps the children with things regular teachers can't deal with.
Franken Fran (comedy, supernatural, sci-fi) The.. Err.. Daughter of a famous scientist performs human experiments on people to solve their personal issues. The result is fantastic.
Tripeace (action, gender bender) Guy dresses up to a girl to fight evil.
Godhand Teru (action, comedy) A young doctor with a special talent saves patients from dying.
Tende Freeze (comedy, ecchi, school life, supernatural) Like, some dude can see into the future and shit. Don't remember this one very well.
Rappi Rangai (action, comedy, harem) Ninja dude tries to find a wife for himself but he's really bad at it.
NHK ni youkoso (slice of life, romance)
Don't remember much except a hikikomori, but i imagine people know the anime well enough.
Tsunbaka (comedy, romance) Slightly silly and charming comedy about a girl with issues. Very original.
Ann Cassandra (action, comedy) Revolves around someone who's trying to change the future with a book.
Yotsubato! (slice of life, comedy) You probably know it, charming manga about a slightly hyperactive girl.
Slce of life
Mushishi (adventure, fantasy) Cool dude exorcising thing, to put it simply. Very creative.
Helen ESP (slice of life, supernatural) Short manga about a girl without senses.
Yokohama kaidashi kikou(slice of life, sci-fi) Cute story about a robot girl set in the future.
Amanchu! (slice of life, sports) Another diving manga, this one more slice of life and not as action.
Usagi drop (slice of life, romance) Story about a parent to an adoptive girl, follows him as she grows up. Highly recommended.
Romance
Chobits (romance, sci-fi) It's clamp so that tells half the story. I remember it as really good, but it's been like three years since i read it.
The conditions for paradise (romance, yuri) Can't say a lot beyond the genres. I remember it as good.
Bonnouji (romance, slice of life) Great drawing style, great characters, read it for yourself. Highly recommended.
Fighting
Psyren (action, psychological)
Aiki (martial arts, comedy) Pretty silly, but something i enjoyed a lot.
Vinland Saga (historical (vikings!), action) The manga that was greatly inspired by
Röde Orm, which is an european comic by Charlie Christensen, and the comic in turn was based on the book by Frans Begntsson. The manga is like manga is, romantical and over the top, even moreso than he comic. I recommend both.
Lucifer and The Biscuit Hammer (action, comedy, fantasy) Bunch of people fighting with an evil wizard. Really good.
Bokurano (action, mystery) Kids saving the world in a big robot and shit, also really good.
Fairy Tail (action, comedy) I don't have to describe this, do i? I enjoyed it, but it's very possible it's gone bad. Manga tend to do that when they go on for too long. Also pretty much just better than author's previous work 'Rave' if you were wondering.
Ares (Action, manhwa) A story about a great war and swordfighting.
3x3 Eyes (action, drama, supernatural) Story about a girl withh three eyes and she makes someone her serverant and he's invincible but then they run into trouble.
Noblesse (manhwa, action, supernatural) Vampire manhwa about a really powerful old guy who gets a lot of friends.
Mystery
Detective Conan (mystery, school life, adventure) Sherlock holmes enthusiast solves murders and gets turned into a kid.
Majin Tantei Nogami Neuro (mystery, psychological, supernatural) Demon turns girl into detective. Manga changes genre towards the end and gets more action, which i really didn't like. Still enjoyed it.
Shinrei Tantei Yakumo (mystery, supernatural) Guy who can see souls solve cases.
Horror
