One Piece has a MASSIVE amount of popularity. In Japan. Frankly speaking here it's usually a weird choice. One Piece does basically two things, Random Humor and Fight scenes. They do them completely well (The Humor is decent, but the fight scenes REALLY shine. Srsly), but generally everything else is usually skimped on, at times done decently, and at other times poorly. Character Development is mostly nonexistant, the plot is usually very simple (Again, the CP9 arc was utterly awesome for this), and when you look purely at the characters the villains are somewhat lacking.
One Piece is frankly a manga you cannot take seriously. The world itself is plain weird, and that's nothing to say about how the characters jump around so randomly in characterization, and generally hold to certain archtypes all the time. If I were so inclined I could go into the utter stupidity of some of the designs, but frankly I don't because I'm perfectly aware of the fact that this was the way the author intended. That usually doesn't catch with most people, and the art style is quirky in and of itself. Basically the Japanese eat it up, while most here drop it pretty early.
To draw a certain parallel, there's another manga that takes nothing seriously, and is basically completely a gag manga. Bobobo bobobobo. I utterly loathe it, but others can find it entertaining because they manage to not take that load of crap seriously. I'm generally the type to look to deeply into things, which is why I can't stand that thing...
One Piece passes under my radar because the fight scenes are so Utterly Awesome that it makes up for the gag humor. Hence why I can still follow it. Plus it's one of the few manga I know that doesn't go into training arcs, which I utterly loathe. The abilities are well done without them, though the power boost in the CP9 arc for the top 3 caused me to raise an eyebrow. Those came out of nowhere (I could go into monster... but that was designed to come out of nowhere...).
Also I reread this chapter and found it lulzy that the old woman figured out what was wrong by saying "Tommorow Morning", and noticed her writhe in agony. Apparently seperation is bad. New Crewmate? That would be awesome. Sanji would weep.