Actor Shipping: Predictably, there's the usual contingent of fans who ship Keanu Reeves and Carrie-Anne Moss based on the strength of their chemistry as Official Couple Neo and Trinity and their adorable friendship in shared interviews. They are close friends and have been for years, but that's all.
Alternative Character Interpretation: All over the place given the series's perchance for Mind Screw. One surprisingly popular theory is that The One is not Neo, but actually Agent Smith. Morpheus tells Neo in the first movie that The One was born in the Matrix, possessed the power to reshape it as he saw fit, and he will eventually return and his coming would herald the destruction the Matrix, the end of the war, and humanity's freedom. These powers and feats are not really applicable to Neo, but are fully applicable to Smith, who (as a Program) was born in the Matrix, took over all of its functionality and gained the ability to reprogram it to his will, and in doing so functionally destroyed the Matrix, and as part of Neo defeating him the Machines ended the war and agreed to free the humans that wanted to be freed.
Applicability: One of the main reasons for the franchise's success is that its themes have been able to be interpreted in a variety of ways, from being a religious allegory, to a metaphor about striking out against "the man", to revealing one's true identity (especially helped by the Wachowskis coming out as trans women).
First film: Cypher, the treacherous member of Morpheus's crew, ends up selling out his comrades and Morpheus so he may reenter the Matrix as "someone important" without his memories. Setting up his team to die and Morpheus to be abducted by the Agents, Cypher is fully aware of the machines intending to wipe out the final bastion of humanity, Zion, while beginning to murder the remaining team members with nothing short of sadistic relish.
Resurrections: The Analyst is a manipulative and power-hungry program that usurps control of the Matrix. After he takes over, the Analyst conducts a purge of programs, killing the Architect, the Oracle, Kamala, and Rama Kandra, an event that orphans Sati. Reviving Neo and Trinity to power his new Matrix, the Analyst traps them in new identities and takes pleasure in his efforts to keep them separated. Assuming the guise of a therapist, the Analyst traps Neo within the Matrix, prescribing him blue pills to suppress his reality-questioning doubts. Upon Neo's awakening, the Analyst torments Neo by revealing his scheme before ultimately unleashing a horde of suicidal bots to kill an awakened Trinity. Defiant and lacking remorse for his actions, the Analyst arrogantly declares that he won't be deleted and demonstrates a firm belief in the superiority of control over freedom.
Critical Dissonance: You'd be forgiven for thinking everyone who saw both Matrix sequels loathed them, even though they both turned profits during their respective theatrical runs. But while Revolutions' significantly lower gross lines up with its critical 36% rating on Rotten Tomatoes and 47 on Metacritic,note Users of those sites give it 60% and 4.7/10 respectively, plus a 6.7/10 on IMDb.Reloaded actually got mixed to positive reviews (73% on Rotten Tomatoes, 62 on Metacriticnote And fans gave it 72% and 6.9/10 respectively, plus a 7.2/10 on IMDb.), making Reloaded more an example of Condemned by History than actual critical dissonance at the time (though defenses of the sequels have since emerged as well).
Epileptic Trees: To this day, there are theories that the real world isn't really the real world, but a second simulation built as a failsafe to help control humans that reject the Matrix by giving them the illusion they have discovered the truth and freed themselves. The "Matrix within the Matrix" theory is supported by many who see it as a solution to plot holes and contrivances, while others disagree since such a reveal would undercut most of the franchise's lore and story.
Evil Is Cool: The Sentinels and the agents, but especially Agent Smith.
Among the films after the first one, plenty of people disregard Revolutions and Resurrections; Reloaded has its share of detractors too, but it's much more well-received.
In regards to other media, some don't accept The Matrix Online as canon either. The Animatrix, on the other hand, fared better with fans.
Fandom Rivalry: While the rivalry has largely died due to both films becoming widely recognized and appreciated, as well as many of their similarities simply being a case of Tropes Are Tools. There was a time when it was common to pit The Matrix against Dark City due to their shared themes and unique sci-fi aesthetic. The fact that one found mainstream success while the other was largely regulated to cult film status and obscurity also fed into the rivalry. Some more resentful Dark City fans even accused The Matrix of being a "rip-off" or "dumb-downed" version of Dark City. Although, again, the rivalry is mostly a relic of the past these days as the fandoms have largely come to embrace both films.
LGBT+ Periphery Demographic: The films have been considerably popular with transgender audiences, given the heavy parallels between the film's plot and trans experiences, which was only enhanced by the fact that both Lilly and Lana came out and transitioned years after the first three films were completed which galvanized the franchise's trans fanbase.
Magnificent Bitch: The Oracle is a mysterious sentient program responsible for the third iteration of the Matrix. For five generations, she acted as an ally to the redpills to find "the One" and give them The Prophecy, which led them to believe they would save humanity. In reality, the Oracle was luring the One to the Architect, who blackmails the One into entering the Source and saving the humans plugged into the Matrix, at the cost of Zion's destruction. The Oracle decides a different course of action for Neo, the sixth One, introducing romance into the equation to make him attached to humanity, while assisting Neo to defeat Agent Smith, which would inevitably achieve peace between humanity and the Machines as she had intended.
In July 2002, a woman by the name of Tonda Lynn Ansley shot her landlady in the face. She proceeded to go for the Insanity Plea by claiming that she believed she was in a computer simulation, saying: "They commit a lot of crimes in The Matrix." The really weird part? This actually worked. A year later, a San Francisco man named Vadim Mieseges used the same defense, for the same crime, even. This has led to "The Matrix Defense" being adopted as a real legal strategy.
This previously came up during the Columbine shooting, when some journalists speculated that Harris and Klebold might have been inspired by a certain amount of misaimed Matrix fandom.
Believing that reality is somehow unreal is a common delusion, the Matrix just happens to fit a paranoid feeling that some people have always had ("The Truman Show delusion" immediately preceded it).
In the New 10s and beyond, a number of right-wing groups and their supporters have hailed the Matrix as (supposedly) prophetic, or perhaps even a warning, about how world governments have become increasingly draconian and invasive, and "the Matrix" is the systems of government and media that Hollywood and liberals use to indoctrinate and control people. Morpheus' monologue "the Matrix is a system" in particular has practically become a rallying cry for far-right American conservatives. The Wachowskis are trans women, and hold views that are very much in-line with American liberalism and contrary to American conservatism. That aside, intentional or not the films have a very definite liberal slant to them; the heroes are racially diverse while the antagonists are all depicted as white males within the Matrix, and a great deal of emphasis is placed on personal choice, especially the freedom to control your own mind and body.
Furthering the distorting of the film's message is another misaimed fandom which uses the term "Blackpilled," a spin on "Redpilled," to claim that they've "woken up" to an overtly nihilistic worldview in which they have so little agency that they claim it's better to either kill themselves or attack the people around them, a far cry from the film's actual use of the red pill as a way to signal Neo's newfound sense of agency and the start of his journey to help the people around him.
A somewhat combination of the two above entries, there are groups of right-wing conservatives who choose to interpret the "Red Pill and Blue Pill" dichotomy as a 1:1 literal allegory for Red (Republican) vs. Blue (Democrat) politics. With Neo choosing the Red Pill as "proof" that conservative politics and policies are the true way to freedom and truth. In contrast, the blue pill, progressive politics, will keep them trapped in a false world where they lose all agency to whatever liberal boogeyman they believe is controlling them. As stated, the Wachowskis are very much liberals in real life, and flat-out rejected this interpretation when it was explained to them.
Most Wonderful Sound: Morpheus' voice is oddly satisfying to hear. Despite, or perhaps because of, him mostly "enunciating like a robot" as TIME magazine put it.
Movement Mascot: The character of Neo and the franchise in general made enough impact to create, more than a movement, a religion. This is what "Matrixism" (or "The Path of The One") is about, founded through The Internet and being a tendency during the Turn of the Millennium.
Narm Charm: The Merovingian runs on this. He's a pretentious bastard and he knows it, he enjoys indulging in high culture for its own sake yet is aware that it, like everything in the Matrix, is just a facade. His mannerisms are hammy, overly theatrical, and he likes hearing himself talk a lot, but he owns it so well that instead of being silly he's oddly compelling.
Revolutionary as the series (or perhaps only the first film) was, these movies owe a lot to classic Cyberpunk, anime, fantasy and biblical lore. Many people think The Matrix invented Wire Fu, even though the technique has been used in countless martial arts films decades before the film was made.
The idea of The Matrix as well, being a modern Science Fiction update of Descartes's Demon, The Allegory of The Cave, Vedic notions of Maya, etc. Which had been a staple of sci-fi for decades, including the movie Dark City, which came out just before The Matrix. (Neuromancer and Shadowrun got it especially bad for a while, since they had both been using the term "The Matrix" for their cyberspaces a good decade or more before movie even existed.)
Elements like characters wearing black Badass Longcoats and Cool Shades who fight with fancy Wire Fu and Bullet Time dodges are associated with nothing other than Matrix in popular culture, but all of them were actually popularized by the first Blade film a year before and again had roots in the "cyberpunk aesthetic".
Rather infamously, The Invisibles by Grant Morrison, from 1994, tells the story of an angsty young man who gets trained by a bald man with round glasses and a sexy woman in leather to be the Messiah and unlock his true power to battle the evil infiltrated in everyday life, and also features the reveal of the entire universe being only a simulation. Its been said that issues of The Invisibles were passed on set in between recordings.
Romantic Plot Tumor: The commonly-focused Love Triangle between Morpheus, Niobe and Locke between Reloaded and Revolutions is petty and irrelevant compared to what's at stake.
Sequelitis: The films are generally considered to get worse with each instalment.
Spiritual Adaptation: The franchise is, in some ways, a sci-fi version of Mage: The Ascension, as it's about a group of people who discover that their world is an illusion, unlocking great powers in the process, and are then pursued by just-as-powerful beings who are tasked with keeping the illusion alive.
They Wasted a Perfectly Good Plot: The sequels make it clear that there is a bit of a schism between the Machines and the Programs. Not only is the Matrix full of Exiles (Programs that were deemed redundant and scheduled to be deleted, but entered the Matrix and went into hiding), but there are Programs that exist purely within the Matrix to oversee its functions and seemingly do not have "real" bodies, and they may do things the Machines don't want them to. While spin-off media explores this schism a bit more, in the films the only Programs that significantly influence the plot acting on their own desires and goals are Smith, the Merovingian, and the Oracle. The Programs have the potential to be a third faction in the Human-Machine war and would play a critical role in the conflict due to their influence over the Matrix, but instead they individually pick one side or the other.
Values Resonance: Especially in the later 2010s and on into 2020 and beyond, with many feeling like uncaring governments were simply exploiting them for their labor and wealth (or energy, if you like) and with Lilly Wachowski stating that the metaphor for the realization of being trans is very valid, the films were caught up in the general re-evaluation of the overall Cyberpunk movement and the first one in particular was valued as a seminal film that was important in newly-acknowledged ways.
Visual Effects of Awesome: Sequelitis may have set in, but all four movies have amazing practical and CGI effects. The fight scenes may also count thanks to the spectacular choreography and cinematography.