Before the actual announcements of the licensing and dubbing of Madoka, there had been a joke that 4Kids will license and dub the anime, with all the bowdlerizing and name changing they're famous for. Sayaka's name is changed to Sarah, for instance. Months later, Sayaka's English voice actress is revealed to be... Sarah Anne Williams.
This fan video features a mash-up of Madoka set to the opening song of The World God Only Knows. This is twofold hilarious in hindsight, as the video was made well before the final arc The World God Only Knows which featured Mental Time Travel, also a major part of Madoka's finale, and also because of the fact that, in the Madoka movies, Homura eventually becomes an equivalent to the devil.
Before the last two episodes were aired in Japan, one fan decided to make a trailer for a Madoka Magica movie in the style of an actual film trailer (watch it here). Months later...
April 21, 2011: Episode 11 airs. Homura, having previously stolen a few truckloads of Type 88 antiship missiles from the JGSDF, fires them off at Walpurgisnacht. April 21, 2011: In Real Life, the JGSDF's 6th Surface-to-Ship Missile Regiment, which uses Type 88 missiles, is disbanded.
This series has been compared to Kamen Rider Ryuki. Over a year later, Kamen Rider Wizard was released, which was noted to have similarities to Madoka Magica. The series after that, Kamen Rider Gaim, has Urobuchi himself as the main writer.
One of the fantasies Madoka has about being a magical girl in the opening features her in a skimpy outfit, much to her horror. Another anime took this idea and ran like hell with it, and arguably serves as PMMM's Spiritual Antithesis.
Never mind the fact that the witch Patricia wears a red and blackSailor Fuku, which is the exact same outfit the protagonist of said anime wears.
In the same vein, Magia Record, the Madoka Magica spinoff game, features many magical girls with Stripperiffic outfits. Looks like Madoka got lucky with her outfit...
It's hard to read the analogy between Madoka Magica and female sexuality in the analysis page with a straight face if you've read a Rule34Alternate UniverseDoujinshi where instead of magical girls, the girls become literal prostitutes.
Kyubey only uses girls for his magical girl contracts because he reasons boys just wouldn't be able to have the same emotional range necessary for energy harvesting. Fast forward four years, and a series all about magical boys with just as much emotion as the girls proves him wrong.
Homura and Kaworu from Rebuild of Evangelion are often compared together. The newly released 3.0 + 1.0 gives us one more point of comparison: Kaworu was in a "Groundhog Day" Loop trying to find Shinji happiness, just like Homura was for Madoka.
This picture compared Homura and Lucifel as two black winged angels who can stop time. Cue the movie.
In August 2012, before the Beginnings and Eternal movies were released, there was a hoax where pictures of a fan-made magical girl were posted on the internet. These pictures falsely reported that the magical girl would be a new character appearing in the Madoka Magica movies. The hoax was so widespread that even Gen Urobuchi commented on it. Fast forward to September 2013 and the introduction of Nagisa Momoe. A few fanartistseven drew Nagisameeting the fake character. The kicker? One way to pronounce the hoax magical girl's name is Asumi Kana, which just so happens to be the name of Nagisa's voice actor. And while we're on the subject, Nagisa is revealed to be Charlotte, which means that YunoateMiyako's head,
How about the fansubs that translated "majuu" as "demon", for the new enemies at the end of the anime series? Now there's a reason the official translation is "wraith".
As noted on the Trivia page, Rebellion premiered in Japan on the same date as Doki Doki! PreCure's Non-Serial Movie. A few months later, Doki Doki aired an episode revealing the show's villain originally made a selfish decision to save their loved one. Sound familiar?
Other spin-offs
Puella Magi Kazumi Magica: Before Chapter 4 of Kazumi Magica was released, there was a popular Japanese fancomic for the anime that had an Original Character named Jubey. He was an all-black version of Kyubey. Kazumi Magica's Jubey isn't an all-black version of Kyubey, but it's close enough to be funny.
Black Comedy variant. In Chapter 6 Kazumi tries and fails to turn a witch back into a magical girl. Similar to Jubey's example, a fanfic had already done something like this.
Puella Magi Suzune Magica: Drakengard 3 was a game with character designs inspired by Madoka Magica and features a cold blooded albino in all white who slaughters other more colorful girls in order to prevent the end of the world. The premise of Suzune Magica is very similar.