Too many favorite manga to count so here are some random recs:
Teppu was a great inversion of the battle shounen protagonist while also showing some realistic MMA training/fight scenes, though it ended too suddenly and I doubt it will be getting an official translation stateside.
If you liked the movie Edge of Tomorrow, then check out the manga it was based off: All You Need Is Kill. The ending is slightly darker but it's pretty good.
Hinamatsuri has just started getting an official translation, about a mid-level Yakuza who has to take care of a girl who literally landed on his head after time-warping from a distant future. The story is a lot more funny than it sounds, trust me.
I'll second @imhungry on 20th Century Boys and Monster. Also check out Master Keaton for the artist's older work set around the Cold War. All good stories by Naoki Urasawa, though they each span hundreds of chapters so it'll be some lengthy reading.