Joss Whedon just suggested to Marvel that there should be a Bigger Bad plotting behind the scenes which enabled Loki to conquer the Earth. And that someone should be Thanos the Mad Titan. And all the executives just rolled with it.
Robert Downey Jr. requested for Gwyneth Paltrow to be included as a way of exploring the Potts/Stark relationship that was established at the end of Iron Man 2. Whedon agreed, because "you should always, given the opportunity, put a Gwyneth on-screen."
Backed by the Pentagon: Averted. The Pentagon said they "couldn't reconcile the unreality of [S.H.I.E.L.D.] and our place in it" (to elaborate, it's left ambiguous as to whether S.H.I.E.L.D. is a national or international agency, and the Pentagon didn't like the implication that the US military would answer to anyone other than the US government) and thus declined involvement in this movie. However, the US Army did give their involvement.
Arguably it gave one to Galaga; a webcomic about the game started up after the film's release.
In the comics, Hawkeye gained his own (very successful) title as a result of the film's popularity.
And the favorable reception of Mark Ruffalo's portrayal of The Hulk led to Marvel planning a sequel to the 2008 film, where none had been planned before.
And of course, Shawarma enjoyed a massive boost in popularity as well after the movie came out.
When Hawkeye was given his own book as a result of his popularity from The Avengers, fans immediately began clamoring for Black Widow to get her own book, too. First issue dropped in January 2014, just a few months before Captain America: The Winter Soldier.
The film originally opened and closed with a set of Book End scenes of Agent Hill reporting to the World Security Council on the Avengers and on Fury's decisions, but this was scrapped because it didn't mesh with the tone of the film.
One of the deleted scenes centered on Cap would've shown newsreel footage of him fighting in WWII, complete with Steve inserted into old stock footage of the war via greenscreen.
Chris Evans: played straight for the movie (he shaved off his mustache and beard to play the role), but averted in the post-test-screen pickups after Evans had regrown his facial hair for Snowpiercer. Rather than have to shave all over again for just a couple of scenes, Cap's face was concealed by a prosthetic or by his hand (most notably in the end-of-credits stinger in the shawarma restaurant).
Tom Hiddleston has naturally blond curly hair. As in Thor, it's straight and black here.
Despite his reputation for killing off loved characters, Joss Whedon has stated that Agent Coulson's death was not his idea, and was something that was decided on from the very beginning.
Marvel all but explicitly stated Edward Norton's attempt to do this was the reason he got Darrined out of the movie. Due to this bad blood, Mark Ruffalo called Norton personally before accepting the role in order to be sure he wasn't stepping on his toes.
Fake Russian: Not only Scarlett Johansson (who does speak surprisingly good Russian), but also Jerzy Skolimowski (Polish) as a corrupt Russian general interrogating her in her first scene.
Not Screened for Critics: Despite the movie's immense popularity and success, not every Blu-Ray reviewer that requested an early copy received one.
The Other Darrin: Ed Norton was originally going to reprise his role as Bruce Banner from The Incredible Hulk, but negotiations broke down. Mark Ruffalo replaced him, making him the only Avenger actor to not appear in a previous film as his character.
So My Kids Can Watch: One of the main reasons Mark Ruffalo signed on not only to play Bruce Banner but, thanks to motion capture, The Hulk as well. Subverted when his daughters were too terrified to watch their father transform into a giant, green rage-monster.
Mark Ruffalo: My daughter was saying, "Why do you want to kill that girl, Papa?" She really thought I turned into the Hulk. I had to leave the theater to convince her that it wasn't me.
The shawarma bit was also his, so by proxy he threw in the entire second stinger.
Also, the Hulk bringing Iron Man back to consciousness by roaring at him was improvised by Mark Ruffalo during his motion capture performance.
The German police car skidding on its front end after Loki blasts it was a complete accident, as it failed to flip over initially.
As Joss Whedon noted, the "That man is playing Galaga!" line was ad-libbed by Robert Downey, Jr., and worked so well that Whedon decided to dub in an image of Galaga on "that man's" console as the scene's punch line.
In addition, a lot of stuff about Captain America's adjusting to the 21st century was left on the cutting room for time and for the future Captain America sequel, most notably a scene where he would have met a now very old Peggy Carter.
Similar to the above, Whedon supposedly had a detailed backstory for Hawkeye written up, but was unable to even reference any of it due to time constraints. And, during the early planning stages (back when they were still writing Iron Man 2), Hawkeye was envisioned be depicted as a circus performer trained by supervilains who manipulate him into fighting the team, essentially a modernized version of his 616 origin story. At another point, he was planned to debut in Iron Man 2 as a S.H.I.E.L.D. agent who works closely with Widow and Fury.
One draft of the movie had it taking place from Tony's point of view.
Another draft, one of Joss's first when he came onto the project, would have done something similar, but with Wasp instead. He decided that too much time would end up being dedicated to this seemingly new character that he realized it would hamper the film. As there was no way to explain her, he had to cut her out, sadly, despite her being one of his favourites.
An alternate opening and ending frame the movie as a flashback from Maria Hill, allowing them to simultaneously flesh out her dislike towards Fury's methods yet her undying loyalty to S.H.I.E.L.D.
There were plans to insert the Oscorp Building from The Amazing Spider-Man, but by the time the CGI model for the building had been finished, the Avengers skyline was already complete.
The fight between Hulk and Loki originally lasted a little longer, with Loki trying to use Self-Duplication to confuse the Hulk. This scene proved too expensive to make it past the animatic stage. Banner's line that "You could smell the crazy on [Loki]" was intended as a setup for how Hulk wins in this scene, figuring out which Loki was real by his scent.
At one point, there would have been a more physically active villain fighting the Avengers, presumably as The Dragon to Loki. Joss had refused to say who this will be, however, in the hopes that at some point the mystery villain will be able to make an actual debut.
Chris Evans plays Captain America, but also played the Human Torch in the Fantastic Four films. The Human Torch is the only member of the Fantastic Four to have never been an Avenger (not counting Cap's brief "Secret Avengers" during Civil War, which isn't an official Avengers team). The Thing is currently a member and was a member in the past, while Mr. Fantastic and the Invisible Woman joined during Inferno.
As mentioned above, the Human Torch was the only standard Fantastic Four member to not join the Avengers, and is in fact the only Stan Lee created character to have never done so. There have been many stand-in members of the Fantastic Four over the years that have also been Avengers: She-Hulk, Incredible Hulk, Spider-Man, Wolverine, Luke Cage, Crystal of The Inhumans, Namor, and Ant-Man II.
The original, World War II-era Human Torch was also a member of the Avengers even though he isn't as famous.
In the Fantastic Four The End mini-series, Johnny is the leader of the Avengers in the future. There have been other alternate universe versions of Johnny that have joined but the main 616-universe version has yet to receive membership.
There was a female Galactus Herald also named Nova. They aren't related in any way.
Screwed by the Network: The first issues (of the Lee-Kirby era), translated in Spain. For some reason, Avengers #9 was not published, they moved from #8 to #10. Initially, nobody noticed anything wrong (at that point, Status Quo Is God), but in later issues fans began to notice recurring flashbacks about the death of a "Wonder Man", which was not in any of the issues they had.