Based on the resemblance of the Anthonies, the very first monsters Madoka and crew encounter, to the Pringles mascot. (In episode 8, Kyoko eats canned potato chips very similar to Pringles. Ascended Meme?)
Kyubey stares into your soul. /人◕‿‿◕人\\ Explanation (with spoilers!)
The series has taken the staple Mentor Mascot of the Magical Girl Genre and made him/it into something rather nefarious. Kyubey will grant you a wish if you make a contract with him by becoming a magical girl and hunting witches (which actually has bad consequences in the long run), and if you don't make a contract with him, he'll pester you until you do, brandishing one and only one facial expression. Creepy as hell.◊
"I don't understand this at all" - said by Kyubey quite a few times emotionlessly when he fails to understand why humans would consider certain traumatic experiences or revelations traumatic.
Ume Aoki, author of Hidamari Sketch and character designer of Madoka Magica, is well-known for her Super-Deformed "widefaces". However, being a GRIMDARK anime, Madoka Magica contains no widefaces. The fans' desire for widefaces was, in an image macro, combined with the Inception meme "We need to go deeper." Eventually, an Inception×Madoka Magica crossover video was made.
Homerun-chan Explanation
Fan Nickname for Homura derived from the Japanese spelling of her name, which sounds like "home run" (homuran). Born in 4Chan.◊
Episode 11 softens it somewhat: It's shown that her body was found.
"If I wished for it, would Kyubey let me fuck him/her/it?", accompanied by a cropped image of Kyubey porn. And yes, not only does it exist, there is also a disturbing large amount of it.
Misspelling "Walpurgis Night", e.g. Whatsburger Night, Walmart Night, Walrus Night, Walt Disney Night, BrazilianNight, Walgreens Night...
"That won't be necessary" Explanation
Homura's Catch Phrase, used on 4komas whenever Kyubey is about to convince Madoka to make a contract in exchange for solving a trivial problem, like forgetting her homework or lunch, or running out of shampoo. Usually accompanied by Homura delivering said item and/or beating/shooting the crap out of Kyubey.
In Episode 8, it is revealed that Homura has the ability to stop time, much like Dio Brando and Sakuya Izayoi. The fanbase, naturally, has run with it. Best shown in this video
In Episode 4, Madoka finds Hitomi being controlled by a witch. When Madoka attempts to run away, Hitomi stops her by slamming her in the stomach. Now most fanart with her in it somehowinvolvetummypunching.
After the finale came out in April 2011, there's suddenly a lot of noise about NAKED LESBIAN SPACE HUGS and Magodka/Godoka/Madokami.
The Church of Madoka/Madoka died for your sins./Do you accept Madoka as your Lord and Savior?Explanation (major spoilers!)
Not only was there much symbolism on Madoka-Goddess taking the burden of the world's despair upon her to purge the world of witchy evil, but the episode also happened to air on Good Friday...
Serial Experiments Madoka/Homura May CryExplanation (major spoilers!)
Madoka rewriting herself out of existence like Lain for the former and the latter when Madoka's wish caused beings referred as demons rather than witches to appear.
I am Penitent Gretchen, or rather, Kriemhild Gretchen as she should have been.Explanation (major spoilers!)
Kriemhild Gretchen's idea of salvation is absorbing all life into her barrier, whereas Penitent Gretchen's idea of salvation is preventing witches from existing in the first place, so magical girls that are due to become witches instead go to Heaven with her. Thus, Penitent Gretchen's idea of salvation is preferable to Kriemhild Gretchen's. Also a reference to one of Gandalf's lines in The Lord of the Rings once he comes back as Gandalf the White, or "Saruman as he should have been."
The finale is often referred to as End of Madoka due to the similarities between End of Evangelion and it.
Mami and her amazing barrage of rifles could be put in a format similar to Archer's Unlimited Blade Works. Same with Sayaka's cutlasses. The best example is definitely episode 11, where Homura pulls an Unlimited Every Military Weapon Works...
Due to the large Les Yay aspects of the show, Homura's interest in Madoka is ampped Up to Eleven in this picture meme turning her into a Memetic Molester. Molesting, peeping, panty stealing, stalking and more... Nothing will stop Homura in her quest of Madoka. And for some mysterious reason she has an odd Verbal Tic of "homu" and/or "homu homu". In later ones, she will start wearing Madoka's panties on her head...
Then after the finale, a whole slew of fanart appeared depicting goddess!Madoka turning the tables on Homura, usually by using her omniscience to peep on her.
Tiro Finale (Physical)note This one's a reference to a little known 80s Al Pacino flick known as Cruising, and in particular a scene where a guy who the Japanese have dubbed "Tengaron (Ten-Gallon) Gentleman" (a.k.a. "the guy who REALLY likes Mami-san") bitchslaps someone. The above meme is the name they've given to the bitchslap in question. Also, Tiro Finale has become the name of any form of Mami attacking physically, or brutalizing Kyubey from the 'everybody hates Kyubey' meme above.
Mami is the most well-endowed Puella Magi, and the mispronunciation of her name kind of sounds like "mammary." (The correct pronunciation sounds more like "mommy")
LOVE ME DO! ↖( *´ 3`*)ノ Explanation
A background line that became completely entangled with Sayaka and her shipping partner(s).
Cake Planet. note For a little while, there's been an image◊ circulating around the Internet of a hypothetical localisation by 4KidsEntertainment, censoring the infamous scene from episode 3 by claiming "Mary" is actually an alien and returning to the "Cake Planet". Because 4Kids dubbing such a dark, tragic, and violent anime the way they normally handle things would be hilarious.
I was... such a fool/I was... such an idiot: note Sayaka's last words before she turns into a witch, said with this face◊ which is usually joked about◊. Common jokes include comics of her experiencing encounters that are not particularly serious, and yet still saying this line with the same face.
The dub version of what Sayaka said to Madoka in the 1st episode.
Mami is forever alone/lonely Mami is lonely. Explanation
Unlike Madoka/Homura and Kyoko/Sayaka, Mami isn't part of any obvious pairing in the anime. Can end up as a "Funny Aneurysm" Moment in the PSP game because this meme is the thing that turned Mami into a witch.