The Internet is awash with criticisms (or is that praise) of how Star Wars Episode VII: The Force Awakens borrows, steals, homages, references, archetype-uses or parallels from Star Wars Episode IV: A New Hope.
What are those similarities?
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In rough order of appearance, here's the list. Note that a lot of these happen in a significantly different order between the two movies, so depending on which movie you're thinking of some things might seem out of place.
The film starts with:
a huge Star Destroyer moving slowly and ominously into view.
The action starts on a desert planet:
Tatooine vs. Jakku
The young protagonist, who turns out to be very strong in the Force, has been left on the desert planet, lonely and dreaming of more, with no knowledge of his/her parents:
Luke vs. Rey
The protagonist meets a droid, frees it, and performs maintenance on it while they talk:
Luke cleans R2 and removes his restraining bolt, Rey cuts BB-8 from a net and straightens his antenna.
Said protagonist is subsequently forced to leave said desert planet
in a spaceship called the Millennium Falcon.
Stormtroopers in search of vital information they need:
Plans of Death Star vs. Map to find Luke Skywalker
Stormtroopers destroy innocent inhabitants in search of that vital information:
Uncle Owen and Aunt Beru’s farm and Jawas vs. village of Tuanul
Said information is hidden in a droid when the information carrier is about to fall into Imperial hands:
Princess Organa hiding Star Wars plans in R2-D2 vs. Poe hiding the map in BB-8
The one who had been carrying the information is captured by the Villain and tortured for their knowledge:
Princess Organa being tortured by Vader for the location of the rebel base vs. Poe being tortured by Kylo Ren for the location of the map
A stormtrooper takes off his helmet and says, "This is a rescue.":
Luke Skywalker to Princess Leia vs. Finn to Poe Dameron
The search for information is headed by the featured Villain of the film, who has a mask, heavy breathing, deep voice, follows the Dark Side of the Force, wears all black, and uses a red lightsaber:
Darth Vader vs. Kylo Ren
Said Villain holding someone off the floor by their neck:
Vader and Captain Antilles vs. Kylo Ren and his subordinate
There’s a real Big Bad hiding behind this villain:
Emperor Palpatine/Darth Sidious vs. Supreme Leader Snoke
There is a military commander with no force power but a similar rank, alongside the main villain:
Governor / Grand Moff Tarkin vs. General Hux
Han Solo is confronted over money-related issues and attempts to "talk his way out of it":
Greedo (also Jabba) vs. the 2 groups of space pirates
The Millennium Falcon is caught in a tractor beam and brought on board another vessel. Those on board the Falcon attempt to evade capture by hiding in a compartment underneath the floor:
Han, Chewie, Luke, and Obi-Wan (successful) vs. Rey, Finn, and BB-8 (unsuccessful)
Han says, "I've got a bad feeling about this":
In the trash compactor vs. when he is trapped by the two gangs
Han talks about the Force, using flowery language:
"Hokey religion" vs. "Mumbo-jumbo"
The bad guys constructed a powerful weapon/base capable of destroying (an) entire planet(s):
The Empire built the Death Star which destroys Alderaan vs. the First Order built Starkiller Base which destroys the Hosnian System
A daring rescue is attempted from this base shortly before the final battle.
Princess Leia vs. Rey
The final battle of each movie results in the destruction of the aforementioned planet-destroying base, saving the day with mere moments to spare:
Luke destroys the Death Star vs. Finn, Rey, Han and Chewie destroy the Starkiller Base
The bad guys also do away with part of the galactic government:
The Emperor dissolved the the Imperial Senate vs. Starkiller Base destroyed the capitol of the Republic on Hosnian Prime
The protagonist is given Anakin Skywalker's lightsaber by a friend:
Luke gets the lightsaber from Obi-Wan Kenobi vs. Rey gets it from Maz Kanata via Finn
There is a cantina full of unique aliens and strangely-dressed humans, with strange music playing, where plans for transportation off planet are discussed:
Mos Eisley vs. Takodana Castle
One of the protagonists abandons the crusade out of desire for self-preservation (considered selfish), but later return to save a friend:
Han and Chewbacca staying out of the Battle of Yavin until the last moment vs. Finn nearly running off with the two aliens from the tavern
C-3PO has issues with his left arm
His left arm was ripped off by Tusken Raiders (Sand People) in the first Star Wars film. In this film his left arm is red because it is a replacement arm due to circumstances that are not mentioned in the movie.
Things with "Star" in their names:
Death Stars and Star Destroyers vs. Starkiller Base
A force user sneaks around a large cavernous room while unaware stormtroopers pass nearby, then pulls a lever:
Obi-Wan on the Death Star vs. Rey on Starkiller Base
The Villain and the newly reunited father figure / mentor share a pivotal scene while the other protagonists watch helplessly, and then scream:
Darth Vader killing Obi-Wan vs. Kylo Ren killing Han Solo
X-Wings must do a trench run over the giant superweapon.
Political tensions between evil black-masked Force wielding villain, and military top brass:
Vader and Motti vs. Kylo Ren and Hux
Masked villain holding someone off the floor by their neck:
Vader and Captain Antilles vs. Kylo Ren and his subordinate
Someone is left for dead in a trash compactor:
Leia, Han, Chewie, and Luke nearly die in a trash compactor vs. Captain Phasma gets sent (off-screen) to one
A protagonist flies the Millennium Falcon while another protagonist shoots the gun and destroys TIE fighters, and gets cocky about it:
Leia flying, Luke and Han shooting vs. Rey flying, Finn shooting
The reclusive, wisened Jedi being sought after has prominent facial hair
Gandalf vs. DumbledoreObi Wan Kenobi vs. Luke Skywalker.
Despite the destruction of the super-weapon and the winning of the battle, we do not witness the death of the main villain.
Darth Vader escaping in his Tie Fighter vs. Kylo Ren presumably being rescued by Hux at Snoke's request
R2-D2 carries important secrets that aren't accessed until the end of the movie:
R2 has the Death Star plans vs. R2 has part of the map to Luke Skywalker
The wise old Jedi master finally returns, having previously disappeared after their student turned bad:
Obi-Wan had disappeared to Tatooine after Anakin turned bad vs. Luke had disappeared after Ben Solo turned bad