You've heard of them: Naruto, Bleach, One Piece, among others. If you live in America, these are probably the first anime you've ever heard about, before anime picked up in the west these last few years. I don't have much experience to base my opinion, but I've always been put off by series like these. Anime critics in general have mixed opinions based on the series in question, usually opting to curse a few like Naruto while praising others like One Piece. In this regard, I am single-minded in that they all are not worth my time.
The first issue I take with a lot of these shows is the time aspect. I can respect a 23-56 episode show, just by knowing it is consistently good for that long. Shows lasting 11-13 episodes, with some exceptions, are quick cash grab attempts, so while they can be entertaining, the writers aren't ambitious enough. Shows lasting more than 56 episodes usually are the type where the story becomes a self-perpetuating machine. Pokemon (before Sun & Moon) had nothing outside of the established order: Catch new regional Pokemon, find a rival who fights with strength instead of friendship, fight team rocket on the way, get 8 badges, defeat the rival when it finally matters, lose to the pokemon league. When you can write an entire season of a show in 2 minutes, there's something wrong with the story. I'm not saying all popular shows follow such a formula, but when so many do, it taints my opinion of the shounen genre (which most of these shows inhabit).
I guess another part of these shows that I don't particularly like is the tropes they choose to incorporate. When I go to watch anime, I don't care to watch someone's tragic backstory flash before their eyes every episode. I don't care about childish rivalries. I don't care about a fight if I feel it's just a fight. There has to be some reason for me to care. Why do I care about Okabe's problems in Steins;Gate? Because time travel is awesome and I want to see how time travel can help him. Why do I not care about Okabe's depression in Steins;Gate 0? Because I'm screaming "Use your time machine dammit" at him constantly. I'm not invested in the characters standing around having Christmas parties when I came here for the time travel.
↑
Would you rather watch this
or this?
↓
The thing is, It's not just a curse popular shows have. I fully enjoyed Hunter x Hunter and Fullmetal Alchemist, both top rated shows. And the reasoning is simple: Hunters are awesome, and alchemy is awesome. Hunter x Hunter, being over 140 episodes, was very prone to being a victim of weak writing and formulaic plots. However, its writer, Yoshihiro Togashi made sure to differentiate his work, keeping the plot fresh and unique with each passing arc. A faithful adaptation was key to making the story as good as it was, and some of the most popular shows are hastily adapted from their source material, creating filler. The first Fullmetal Alchemist anime ran into this problem, which is why it is generally viewed as the worse version of the story.
As always, the best shows will be those that fit best to your own ideas and tastes, so maybe this is all because I'm just different from everybody else, and my tastes don't align with yours.