I think there are a lot of other stories that are "great" just like One Piece is "great". But considering One Piece is a long time running series with continuous development of story, characters and worldbuilding, with a fleshed out plot and lots of humor, adventure and drama, there is none similar or close to it.
There are though the "great" other stories that are "great" on its own without being compared to One Piece. People already named them but such as Berserk for example. It targets a different audience, is way darker and more mature. But the way it is presented and told, the story itself is a masterpiece on its own.
There are quite the series I enjoyed reading as a whole and hyped with them or had fun reading them, such as:
- Assassination Classroom (Though not every class member got much representation, the main characters were awesome and it was really funny and enjoyable)
- My Hero Academia (it rises in popularity more and more, and though some arcs and plots were boring sometimes, the story is improving as well as the art style and characters)
- Black Butler (honestly, this is one of the stories that you think are funny and full of adventure and cool plots until it hits your head on hard, cold concrete and shakes you back into reality. The way the story is being told and unraveled is amazing)
- I don't want this kind of Hero (this is a Webtoon, but from the feel and the characters it hits close to the amazing character diversity of One Piece in my opinion and it is just as ridiculous and sadly serious. The plot isn't as deep and feels a bit random but it is a fucking good read and the art style rounds it up even more, can definitely recommend)
There are some other stories I enjoyed reading but since this is a thread to compare some to OP, these are the ones I wouldn't compare in levels to it, but similarities and thought-through plot