The rather abrupt end of the Substitute Soul Reaper arc was the result of this. Kubo mentions that storylines had been planned for Ichigo's other class friends, but were then shot down by Shueisha who ordered him to speed up the schedule and introduce the Soul Reapers. Whether or not this was an improvement is a major YMMV in the fandom.
The entire Arrancar Arc was plagued by this, as the Arrancar characters' popularity resulted in editors requesting an increased role - in turn leading to the arc running much longer than Kubo's initial intent. For better or worse, the pacing has been much brisker since Aizen's defeat.
Uryuu Ishida is known as Arrowlad. When his father entered the storyline (arrows first), he promptly gained the nickname Arrowdad.
Ichigo's white inner hollow is often called Shirousaki (shirou = white) as a play on Ichigo's surname (Kurosaki, which means Black Promotory). He's also referred as Hichigo, short for Hollow Ichigo.
The Nameless Leader of Vandenreich has earned the name Mein Furher from those that dislike his chapter inspired name Buckbeard... 'cause he has no beard.
With the revelation of his name, people are quickly calling him "Bach-beard"
Yamamoto is Old Man Genocide
Blondie for Haschwald (at least before his name was revealed)
Colonel Sanders and Commissioner Gordon for the still unnamed Quincy With Glasses
In the French fandom, Hitsugaya is known as "La Crevette" (The Shrimp). The origin is unclear, maybe it has to do with his hairstyle or more likely a reference to his height.
Fountain of Expies: Studio Pierrot liberally recycles aspects of Aizen's character into their own antagonists for Bleach, in no small part due to the impact he made to the series. It's also inverted; instead of other series taking their cues from Aizen, Studio Pierrot used Aizen as a template for anime-exclusive villains of the same series.
Not to mention Shusuke is suspiciously similar to Sosuke.
Kouga Kuchiki of the Zanpakuto Unknown Tales arc? A Person of Mass Destruction that gets sealed away for years, mistreats his subordinates, betrays his most loyal ally by stabbing through their chest and possesses a sense-manipulating illusion ability, He faces his defeat at the hands of someone "beneath" him.
Kokuto from Hell Chapter, the fourth film? A villain that pretended to be an ally, faked his death, revealed his betrayal by stabbing someone nearby and butchering a person close to the protagonist. He faced defeat through the best attack of The Hero's super-powered form and gets sealed after assuming that he'd won afterward.
Even the manga is getting in on the act. Shukuro Tsukishima is a constantly smiling Manipulative Bastard with a unique special ability that he uses for Mind Rape; he even resembles Aizen by a bit. Inverted in that he's working for Ginjou, who ironically is much like an evil Isshin, and Tsukishima himself is resembling Gin with every Mind Rape he commits.
Masashi Ebara does the voice for the Big Bad in the first Bleach movie. Of course, it's hard to take him seriously once you realize that same voice actor is shouting about the Glorious Springtime of Youth as Maito Gai in Naruto.
Shinichiro Miki, who voices Urahara Kisuke, did the voice of Mizuki in Naruto, the man who revealed the Kyuubi secret to Naruto in episode 1. He also voices Roy Mustang.
Ichigo gathers a ragtag group of friends from his school to enter another world and fight unsurmountable odds to rescue a friend, continually getting stronger after each opponent up to a climactic clash that ends with an Anticlimax. The Soul Society arc, or the Hueco Mundo arc?
Even the details are similar. It all starts when two uniformed baddies, one rowdy and one emotionless, show up in the human world. Defeated by them, Ichigo goes through Training from Hell to gain new power. Once on the other side Ichigo gains a small, friendly tagalong, while one of his True Companions gets to defeat the murderer of their mentor.
Ichigo fights the stoic guy who kidnapped the damsel in distress. He is temporarily defeated, only to launch into a new Hollowfied form and temporarily curb stomp them. The next fight is him and others being manhandled by Aizen as he explains how weak they are.
The hero must use a Dangerous Forbidden Technique that will make him lose his powers forever. Supposedly. The badguy survives and heals anyway, but is taken out of the story for now. As the comic still has not ended, it may recycle the story about regaining powers one more time as well.
As a matter of fact, Ichigo did get his powers back, in the very same way he got them in the first place. Only this time, the recycling was intentional. And it was epic.
A white haired villain wants to take over Soul Society because he and his kind were exiled long ago. The Bount arc (Jin Kariya, Bounts), or Memories of Nobody (Ganryu, Dark Ones)? The English dub even uses Troy Baker as the same voice actor for both characters.
The Third movie, Fade to Black, is intentionally filled with deja vu to repeat lots of older scenes throughout the series. Though the Hollow parasite that takes over Rukia's old friend is just simply recycled.
The Hero is confronted by a group of superpowered humans who continuously trick him, but after the final battle, it's revealed that the hero's Trickster Mentor was behind it the whole time. His intention was to make the hero think about how he couldn't always use power to win fights. Am I talking about the beginning of the Bount arc, or Chapter Black from YuYu Hakusho?
While the latter example is much more dramatic, both the Zanpakto Rebellion arc and the Hell Chapter movie involve the villain tricking Ichigo into using his Hollow powers to break through a seemingly indestructable prison.
The Other Darrin: In the American dub, Chad's and Ikkaku's voice actors had temporary fill-ins for Real Life reasons, but Kaien, Kenpachi, and Urahara all have permanent Other Darrins without much explanation. This is not helped by the fact that no seiyuu in the course of the show in Japan had to be replaced for more than temporary absences.
What Could Have Been: The first draft for Bleach was very decisively different than Bleach is as we know it today: Soul Reapers shrunk when exerting too much power. This happens to Rukia in "chapter zero" where she is then washing herself with Ichigo's toothbrush in a coffee cup. Ichigo seems far more interested in girls, especially Inoue (he denies it of course). Orihime dies at the beginning, being killed by her hollowified father, but instead of going to Soul Society decides to stay with Ichigo to cheer him on. This version was shot down by the publishers.
Other changes mentioned by Kubo include that Rukia was meant to be a more central character, as in the lead character, and that most Soul Reapers used firearm-themed zanpakuto rather than swords whereas Rukia used a scythe. The sketch of Rukia with a scythe was used as a base for the "Dark Rukia" in the third movie, Fade to Black I Call Your Name.
The Menos Forest mini-arc would have been in the manga had it not been for time constraits forcing Kubo to cut it.
Kubo initially envisioned Mayuri as a fairly flat personal enemy for Uryuu, who would finally vanquish Mayuri after a series of encounters. However, Kubo then began plotting out the final arc even before the Soul Society arc had finished and realised that the Arrancar Arc afforded him the opportunity to develop Mayuri's character as an example of how a truly evil individual can be still useful to an organization that is, overall, on the side of good-ish.
When in an interview about Shinji, Kubo mentioned that he had wanted to do stories for Ichigo's other classmates as well—directly implying storylines for Keigo, Tatsuki, and Mizuiro—before the executives told him to move up the schedule and get to the Soul Reapers.
Urahara was originally going to be The Big Bad of the series, not Aizen.