Before becoming a part of the manga fandom, as a resident of the U.S, I saw One Piece as a cartoon that was more suited for kids. The fact that Naruto and Bleach is more popular than One Piece here among the "Big Three" is mostly the fault of the American cartoon company, 4Kids, who licensed One Piece and heavily censored and edited the anime. (please, it's not even close to what's it's supposed to be) When I learned that One Piece is the best selling manga in history (the series sold over 280 million volumes sold as of the end of 2012, with the initial release of volume 61 breaking the record for the first print publishing record of all books in Japan "Harry Potter and Order of the Phoenix") as well that 88% of its readers in Japan are adults, it gave me the motivation to seriously start reading it. The experience was a pure joy and it's been stuck in my head ever since. Each arc gets more and more exciting as you read on and everything from epic battles to comedy relief brings the characters to life. As one of the comments said, it's all about the journey and not the destination. And it's a very epic journey. (in fact, at one point in the manga, Luffy says he doesn't want to know where One Piece is right away or it'll make the adventure boring) That's why you have to experience the adventure thoroughly to properly understand how good the series actually is. I myself didn't really get why it was considered one of the best after reading several volumes. Continue on without question and you won't regret it. Personally I found the Enies Lobby Arc the climax of the series; after that I considered One Piece to be one of my top favorites and certainly the best mainstream shonen manga.
A lot of ideas for manga are based on real life examples with a fictional twist. One Piece brings together pirates vs. marines with mythical beasts and devil fruit powers. This allows for a lot of leverage for the design of many interesting characters. We have our protagonist, Luffy, a rubber man who's ability to stretch combines close combat with long ranged attacks (I mean seriously, who else but Oda would think of this) and his crew who goes up against a multitude of villians with their own unique devil fruit powers and developed abilities. The fights in this story become more and more epic as the challenge becomes tougher and tougher with the result of the characters becoming stronger each time as well. Not only do each individual's abilities evolve, their teamwork becomes phenomenal. The creativity put into this series is simply a blend of genius, meaning no one else could've written anything like it.
Oda Eiichiro-sensei was fully aware that his art style might put off some people (that's where some of the bias comes from in America) but as One Piece's popularity grew, his unusual art was shown to be be one of One Piece's selling points. It allowed him the freedom to draw interesting battles, funny scenarios, and bizarre characters. Rather than getting "used to the art," you'll find yourself immersed in it.
Another selling point of the manga is that although there is always the comical annoyance between the crew members, all the members loves and values their crew dearly as all of them have joined Luffy's crew because of some sort of dream; dreams that were inspired by some sort of tragedy they experienced or by some person they have met. You'll find yourself touched by the characters interactions as you see them go through hardships as well as joyful moments, with their dreams becoming the drive force that makes each individual powerful. You'll have fun with the characters as they all have their own role in entertaining the reader; comedy and seriousness is blended together perfectly in series as each one of them has their own very unique personality. This allows for a plenty of hilarious gags intricately put in each chapter. As you observe their adventures, jumping from one island to the next, you'll see the crew always getting into some wacky situation as troublemakers and how they're always ready to be heroes and save anything from a small village to an entire nation. Because of how they always meddle into the affairs of others, the tiny crew starts off as nobodies only to become infamous worldwide as the plot progresses into something enormous.
The idea of many people is that many shonen manga reach its peak at some point and only get worse if the author attempts to keep the series going on for too long instead of ending it, but One Piece has been going on for 600+ chapters and has only gotten more interesting. Oda always knows how to take the series into the right direction. (he says at chapter 597 that the series reached its half point then)