Her character in Guilty Crown has feelings for a boy played by Yuuki Kajinote Ambiguous in canon, but official parodies portray Annie as having feelings for Eren, and likewise covers herself in crystal at one point.
Ascended Fanon: The 3D maneuvering soldier with afterimage effects in the opening actually wasn't supposed to be Jean, but rather a soldier representing humanity. However, given the number of people claiming it to be Jean, the production staff has acknowledged it as so.
Beam Me Up, Scotty!: The first line of the first OP Guren no Yumiya has been misspelled in numerous ways due to Linked Horizon's inexact pronunciation of German and inconsistent fansubs, one common one being "Sie sind das Essen und wir sind die Jäger!" The official spelling is "Seid ihr das Essen? Nein, wir sind der Jäger!".
Blooper: In episode 4, Hannes' uniform has the Survey Corps symbol on it.
In the manga, the same mistake is done with Annie's uniform having the Survey Corps symbol during the scenes where Eren and co. attempt to trap her.
Jokes and theories about Erwin being a Shifter have cropped up after Chapter 57 when he placed his right arm on Reeves' corpse, despite it having been bitten off by a Titan a few chapters earlier.
Creator's Favorite: Hajime Isayama, mentioned that his favorite character is Jean Kirschtein due to his ability to be blunt and say exactly what he's thinking despite the circumstances.
Fan Community Nickname: The Funimation-sponsored cosplay group that met at Anime Expo 2013 used the term 'Troops'; whether this is widely accepted and used remains to be seen.
Fandom Nod: After the production staff liked the idea of Jean being the backflipping soldier in the opening (see Ascended Fanon), Jean was shown performing that exact move as an escape maneuver when his group encountered the Female Titan.
Less prominent, but Ymir is consequently referred to as Freckled Satan. Ironically, there are also people who have referred to her as Freckled Goddess.
"Gesumin" for Armin, when he's being a Manipulative Bastard. ("Gesu" is Japanese for "scumbag".) Coined by Isayama himself, when he posted the original version of the scene where he sports a Slasher Smile while lying to Bertolt about Annie being tortured, showing just how disturbing the original expression was. It was captioned, "This Gesumin....What should I do with it?".
There's also "Shota He-Man", thanks to his blonde bowl cut.
"Geographia" for Frieda Reiss, who was shown in Eren's flashback in chapter 53, due to her Uncanny Family Resemblance to her half-sister, Historia Reiss.
Some jokingly call Historia's mother "Rosa" due to physical ressemblance and her wishing her daughter was never born.
Abe Lincoln, John Marston and Clint Eastwood for Captain Ackerman due to his physical resemblance to them. Also "Kanye", due to early scanlations translating his name as Kaney coupled with his tendency to start lines with "Yo [Insert Name Here]".
Following Darius Zackly's confession that his overthrowing of the puppet monarchy was essentially for shits and giggles, fans quickly christened him as "Dickly".
Hey, It's That Voice!: The anime adaptation is almost a reunion of several people who previously worked with director Tetsuro Araki:
Bryce Papenbrook has admitted to being a huge fan of the anime and that he would love to be a part of the cast list for the English dub. And the best part is that he did end up on the cast list. As Eren.
Promoted Fanboy: Many members of the dub cast, like Patrick Seitz and Josh Grelle, watched the simulcast of the Japanese version. The most surprising example of this, however, is the dub VA for Eren Jaegar: since Funimation was announced to be the English distributor of the series, no one could've expected Bryce Papenbrook, a California-based VA and huge fan of the series, to be announced as the leading man of the anime.
Shrug of God: Isayama does this quite a bit, in combination with his trolling of the fandom. Among the things he has shrugged and left up to the fans or otherwise refused to clarify:
Hange's gender is whatever fans want it to be. (He also invited fans to decide any character's gender, including those with a stated one.)
Rumored to have stated that any and all pairings may be canon if fans want them to be.
Sleeper Hit: Since its debut, it has become one of the best selling shonen manga in Japan and positively exploding with the anime. In 2013 volume sales only the Pirate King survived the Titan onslaught as people furiously bought up the back issues.
Not exactly from Hajime Isayama, but there was an announce that dakimakura of Shingeki no Kyojin would be released. Of course anyone would expect to see Eren, Mikasa, Armin, Levi, Annie and the like, but when one was released...◊
And Isayama strikes again. He was asked to promote a new series so he drew an advertisement band for the first volume. This◊ was the result◊.
With the release of the second Guidebook, "Outside", the cast now have birthdays. Reiner's birthday is stated to be August 1st, which is celebrated as "Yaoi Day" by fans of the genre.
It gets better: Marco's birthday is revealed to be June 16th. That's exactly half of the year.
Isayama strikes again! When a fan at a Q&A event asked what type of woman Levi preferred, Isayama responded by questioning whether Levi liked women and suggested he just likes tall people. (Which covers every single popular ship.)
What Could Have Been: Hajime Isayama first brought his pilot to Shueisha, with the hopes of having it published in Weekly Shonen Jump, but the editor who evaluated his work said that it was good, but not good enough for Jump standardsnote "This is manga, we want JUMP!" being his exact words; then, when Isayama gave his pilot to Kodansha, it was accepted in no time and published at Bessatsu Shounen Magazine, a monthly offshoot of their Weekly Shonen Magazine. The first two volumes sold more than a million copies combined. As a result, Jump, and consequently Shueisha, lost a giant new hit to its biggest rival.
The pilot itself, now called Attack on Titan: Volume 0, is extremely different from the series that we know today. For starters, third-dimensional maneuver gear don't exist in the pilot, and humans are fully capable of "jumping 10 meters" while fighting Titans.
When Annie is called out as the Female Titan in chapter 31, Isayama originally drafted her reaction to be along the lines of a (disturbing) Tearful Smile, as a result of being "relieved" she'd been found out. He regretted his decision of changing it and requested that a similar reaction would be added to the anime.
Isayama had originally planned to kill off Sasha in chapter 36, but later abandoned that idea, it was apparently so brutal that the editor went to the bathroom and cried.
In the same interview describing the initial plot of chapter 36, Isayama stated he originally had Eren knowing all along he could turn into a Titan, but later dropped the idea.
The walls were inspired by Isayama's hometown, which was surrounded by mountains. Isayama wanted to go beyond the mountains, so he transferred his desire to Eren, who desires to go outside the walls and see the outside world.
Isayama revealed that the idea for Titans themselves came from an encounter he had with a drunk person while working at an Internet Cafè. The difficulty to communicate despite both of them being the same species inspired him, and at that moment he considered the most familiar and scary animals in the world to actually be humans.
Mikasa is, at one point, described as "worth a thousand soldiers". This line is lifted from the Tales of the Heike in reference to Tomoe Gozen, a legendary female warrior of Japan.