Back in April, Marvel president Kevin Fiege let loose an unknown Easter Egg that is included in Phase 2 of the Marvel Cinematic Universe: at least one character loses their arm or hand in every single Phase 2 movie. This was made as a tribute to Star Wars, possibly because this is Marvel's second phase, and in the second Star Wars movie (The Empire Strikes Back), Luke Skywalker's hand is chopped off.
Now that Phase 2 is finally completed, we can take a look at every single character who lost their arm or hand in each movie, starting with Iron Man 3...
[WARNING: MAJOR SPOILERS AHEAD]
Iron Man 3 (2013)
In the final addition to the Iron Man trilogy, the leading antagonist Aldrich Killian gets his hand chopped off by a blade hidden in Tony Stark's suit. Thanks to Killian's regenerating abilities from the Extremis, though, the arm grew back in seconds.
Thor: The Dark World (2013)
In Thor: The Dark World, it appears as though Thor's hand is cut off by Loki who suddenly turns against the hero. It is revealed, however, that it was just a trick that they set up together and that Thor's hand being cut off was only an illusion made by Loki. It was still an enormous shock the first time I saw it.
Also, during the final battle, Malekith loses his arm when it is chopped off by a portal. His arm never grows back, but it's not like it needs to. He dies about five minutes after anyways.
Captain America: The Winter Soldier (2014)
Though we don't actually get to see the arm be cut off, we do see the after effects of Bucky's (the Winter Soldier's) horrible accident. There is flash back scene of Arnim Zola installing the metallic replacement arm back onto the brainwashed Bucky after his supposed death in The First Avenger. So though we don't actually see the arm being lost, we do learn about what happened and see the aftermath of it.
Guardians of the Galaxy (2014)
Instead of just losing one arm, Groot loses both of them thanks to an attack from Gamora near the beginning of Guardians of the Galaxy. Fortunately for Groot, the arms are able to slowly grow back while he is transferred to prison. The best part about this particular scene, though, is that Groot seems completely indifferent to the loss of two of his limbs.
Avengers: Age of Ultron (2015)
In Age of Ultron, we witness Ulysses Klaue lose his arm after it is chopped off by Ultron in his rage. Unfortunately for Klaue, he does not have regenerative abilities like Groot or Killian. His arm is stuck being off. It is believed we will see Klaue return with a new, robotic arm in Black Panther or in a later movie like in the comics.
This one was hard to catch unless you were actually looking for it. During the final battle right after Ant-Man leaps into the Yellowjacket armor to destroy the suit, we see Darren Cross/Yellowjacket start to shrink into nothingness. The first thing to go is his right arm, which zips away into his shoulder. Cross is stuck armless for about 5 seconds before the rest of his body shrinks down to nothing.
In Age of Ultron, during the long-awaited Hulk vs. Hulkbuster fight, we see the Hulkbuster's arm come off. After the Hulk stabs an enormous pole in the arm, Iron Man just loses the arm completely and replaces it with a new arm which flies to him. Since it was just the arm of the suit and not Tony Stark or any living character, it is not widely accepted as a character losing an arm, but I'll still include it!