Ask any anime fan what the most irritating thing about anime is and chances are, they'll say that it's filler arcs and episodes. Filler are anime-exclusive stories that typically arise because the creators are waiting for the manga, light novel, or other content on which the anime is based, to release new material so that it can be adapted. The worst offenders are long-running series like Naruto and Yu-Gi-Oh!, but shorter anime can also fall victim to this trap. Filler isn't always terrible - there's actually some that's pretty good - but there's a reason it has such a bad reputation.
The worst filler does nothing to advance the plot or develop the characters and distracts from or contradicts what's meaningful about the original story. Naruto is rife with bad filler, but one of the worst is an arc that deliberately goes against the shows' most basic premise - that Sasuke was Naruto's first friend. Bleach has plenty of bad fillers, but one of the worst introduces a villain that's impossible to care about when Aizen is just about to betray his comrades.
All of the filler on this list is terrible, each in their own unique way. The one thing they have in common is that they are not worthy of your time.
This offender is so ubiquitous among anime that it's impossible to single out just one. Recap episodes might have been necessary - if disappointing and irritating - back when people watched anime on TV, but in the age of the Internet and streaming services, most people are binge-watching multiple episodes in a short span of time. Even when they're watching a new seasonal anime, they can easily look up recaps or go back to parts of the series they've forgotten about if necessary. Recap episodes aren't common anymore, but they make trying to catch up on older shows like Gundam and Fushigi Yugi super frustrating. (Fushigi Yugi, by the way, has at least three minutes of filler per episode.)
Are they skippable? Sure - except that some of them weave in new content between the mishmash of loosely connected clips from past episodes, some of which can be plot important. It'd almost be better if these episodes were entirely filler.
What keeps fans who haven't seen Naruto from checking out the shonen classic? The filler episodes. While some of them are pretty good, others are a complete waste of time. But wasting time isn't the worst sin these fillers commit - some arcs straight up contradict canon.
Yota is a five-year-old from a traveling clan of weather manipulators, but he passed away as a little boy due to poor health. Orochimaru reincarnates him and sends him to Konoha to do some damage, but he ends up becoming friends with five-year-old Naruto and the rest of the Konoha kids, who try their hardest to protect him before ultimately losing him. This could have been heartwarming, aside from the fact that it rewrites Naruto's entire childhood. He claims that Yota was his first friend - that has always been Sasuke, and it's kind of a big deal. Not only does Yota usurp Sasuke's spot, the arc also depicts Naruto being friends with the other Konoha kids - so it doesn't just contradict canon, it contradicts itself.
Yes, that's right, it's time to throw an entire series under the bus. Black Butler II has nothing whatsoever to do with the Black Butler manga, in part because the creators had to figure out what to do with the non-canon second half of the first series. This could have been a great opportunity to deepen the existing characters, and introduce compelling new ones, but instead viewers had to deal with the mega-brat Alois Trancy. Sebastian and Ciel both seem to completely forget about their original goals, and the series devolved into fan service that was occasionally enticing (when it involved the demon butlers), occasionally creepy, and rarely well plotted.
The end of Blue Exorcist was a major disappointment for a lot of fans of the series. Why? Because rather than wait a short period of time for new manga material to come out, the creators opted to come up with an entirely new story, one that heavily contradicted plot points that would come later, which created inconsistencies with the Kyoto Saga sequel that would follow the manga's storyline. The result was a convoluted mess that requires viewers to watch the anime and read the manga to understand even half of what's going on. While there's nothing wrong with experiencing both if you enjoy it, it should never be a requirement.