Naruo had perhaps the most potential, but has gotten screwed up since about the wave-bridge arc. I better not start ranting of this one, because then I'll be writing an entire novel of the things gone wrong.
Bleach also had great potential, but got screwed a bit differently: Adding a hundred new charactes when we can barely keep track of the old ones. A deep, well thought out plot for further character development for the few core-characters would have done a lot, but instead it has gotten to the points where every character gets a chapter or two and that's it, time for a yet another, previously barely mentioned character to get their life-sobstory out. And let's not forget the completely illogical fights, even for anime standards. It's like the writer hasn't ever even met someone who knew anything of tactics or strategy. A 10 year-old who has played a single RTS for 30 minutes could devise better stratagems and these shinigami liutenants and captains are supposed to be expert fighters with age measured in centuries, not to mention the captain-commander who is several millenia old.
Dragonball Z... let's summarize: "Gyyaaah! Power-up from nowhere! Feel my planet-destroying wrath"
7 episodes later, still in the same single fight, planet intact(or not).
"Hahaaa! Looks like I can't defeat you power-up without powering myself up! HAIR GROW AURA TECHNIQUE!"
Repeat ad infinitum, the fighters always pulling out a 'I'm not left handed' or 'Eleventh-hour superpower'-trope, followed by 'I'm not left handed either!'-countermove. Sure, this happens in many anime, but Dragonball is built around this and repeats this more than any other anime I've seen. Add to it the ability to counter any loss or damage by simply making a wish and restoring any damage done (including destroyed planet), we have a bland and boring anime that gets old after the first 4 or five episodes.
Never seen One Piece. And from what I've been told of it, I'm glad.
So, a hard choice between four bad anime, but the final contestants on the merit of sucking less, are Naruto and Bleach. I'm going to give this one to the Bleach, as it had more episodes done well / decently before it began to suck. But none of these four is the best anime.