Seconding Monster and 20th Century Boys. Naoki Urasawa's works in general are worth checking out (at least up to Pluto; Billy Bat was eh).
Here are some recs from my current reading list:
Sangatsu no Lion (aka March Comes in Like a Lion) - shogi, psychological, slice of life. VERY moving. It's been adapted to two live-action movies (part 1, part 2).
Giant Killing - pro soccer; the story is told partially from team manager's point of view and puts a lot of focus on team building , club management, game tactics, mental training etc.
Uchu Kyodai (aka Space Brothers) - space exploration, slice of life. Realistic but very heart warming.
Kounodori - medical (ob-gyn), slice of life. There's a drama version (two seasons).
Theseus no Fune - time travel, crime, psychological, mystery.
Issak (イサック) - historical; about a Japanese rifleman in 17th century Europe.
Gekkan Shojo Nozaki-kun - ingenious parody of the shojo manga genre.