I second Berserk. It's in the mature category, with plenty of violence/the occasional [censored] scene, so it's not for everyone. But the story and the art... wow.
Gundam Eclipse recommended 20th century boys, I agree. Even if it was without any of the actual pictures, the story alone would make me read it.
Out of the popular weekly mangas, I would say One Piece is the best, and it's one of my overall favourites. In my opinion it's leagues above Naruto, Bleach, Fairy Tail, etc. (I read those too, but One Piece is the only one I
really look forward to reading each week).
Full Metal Alchemist... if I could live in any fantasy world, it would be the one from FMA. Definitely recommended (the Full Metal Alchemist: Brotherhood anime is also great, follows the manga to a T, and is one of those rare animes where I thought all the voices fit the characters just right. Wait... never mind, there was that terrible terrible panda voice...)
Dragon Ball is also a great classic to read
. Somewhat silly, and not exactly the best of stories, but it did essentially start the whole shounen genre as we know it today...