Alternative Character Interpretation: The original Expanded Universe novels (and the comic adaptations thereof) actually justify the propensity for humans to grab the Idiot Ball in the films by declaring that the Xenomorph Queens produce a telepathic broadcast which subtly enthralls humans, literally compelling them to subconsciously want to help the aliens breed and multiply.
Catharsis Factor: Weyland-Yutani is eventually bought out by Walmart. The MegaCorp behind so much evil is brought low enough by its own screw ups that it can be owned by a convenience store chain.
Common Knowledge: "Xenomorph" is not supposed to be the proper species name of the creatures. "Xenomorph" is simply a scientific word meaning an alien lifeform, which they use because no one's seen such a creature before and don't know what to call it (i.e. it's the taxonomic equivalent of "UFO"). It doesn't actually have a name but a mere designation: "Xenomorph XX121". It has been given two separate binomial names though, referred to as Internecivus Raptus in some of the home video releases and Linguafoeda Acheronsis in some of the comic books, and the Yautja refer to it as "kiande amedha." It doesn't help that a lot of spinoff material and crossovers directly refer it by that name either.
Creepy Awesome: The Xenomorphs are among the most iconic aliens in science fiction thanks to their Body Horror life cycle and nightmarishly cool, even thought-provoking design by H.R. Giger, which is rounded out by their ability to stalk and kill prey.
Delusion Conclusion: A section of the fanbase is so dissatisfied with the later sequels they prefer to think they're nightmares Ripley is having in hypersleep, which stems from an unused draft of the fourth film as a way to retcon Ripley's death.
Evil Is Cool: The Xenomorphs, whose biomechanical appearance, disturbing life cycle and physical abilities lend to them being highly efficient and memorable antagonists that are among the most beloved evil(-doing) aliens in science fiction.
Alien: Covenant didn't help things with the suggestion that David, an android, created the Xenomorphs. This has been criticized for similar reasons to aformentioned Prometheus.
Thankfully, most Alien media has realized this mistake and instead gone with the explanation from earlier drafts of Covenant: David's "Praetomorph" was his attempt at reverse-engineering his own Xenomorph, which originated from somewhere else.
Xenomorph - Used once or twice in the films, among many other words, to describe the aliens in the franchise, this word stuck as the standard term used by fans. It became used to specifically refer to the films' creatures in merchandise like the comics and video-game spinoffs, and was eventually canonized when Xenomorph XX121 became the official name for the creatures in the Out of the Shadows trilogy, the Alien: The Weyland-Yutani Report, and the Alien: Covenant promotional website (though this "name" is still more of a loose categorization than anything, with "xenomorph" being the zoological version of "UFO" in-universe). This is reinforced in Alien: Romulus when Rook refers to the creature as "XX121 Xenomorph".
Other names for the species used in spinoff media are "Internecivus Raptus" (Murderous Thief) and "Linguafoeda Acheronsis" (Foul-tongue from Hell, Acheron being also the name of the planet on which the creatures were first encountered in Alien).
None of the life cycle stages (i.e. Facehugger, Chestburster, Drone) were ever officially named on-film. They were given Fan Nicknames which simply stuck and wound up being used in some of the expanded universe material and even eventually by the production staff themselves.
Some fans prefer to believe that the third and fourth films never existed, and that Hicks and Newt never died (Ripley's nightmare in cryo-sleep, her last words in Aliens telling Newt they can both dream all the way home).
Some fans feel the same way about the retcons and revelations found in prequels Prometheus and Alien: Covenant.
While it may be due to the crossover between the two, both the Alien and Predator series have overlap thanks to both being '80s sci-fi horror series revolving around monsters, in addition to sharing numerous creators and actors between the two such as special effects by Stan Winston, James Cameron having input and actors such as Bill Paxton and Lance Henriksen.
Terminator has an overlap in interest with the series, owing to also being a violent sci-fi series of The '80s sharing numerous creators and actors with the Alien films, particularly several actors from Aliens and James Cameron. And the fact that both the Xenomorph and Terminator are guest characters in Mortal Kombat games. This also ends up extending to RoboCop, which essentially shares the same community as Terminator, so one could consider the foursome of Alien, Predator, Terminator, and RoboCop to all have the same general fanbase. In addition, both Alien and Terminator had their female protagonist (Ellen Ripley and Sarah Connor) grow into a badass, well-rounded and charismatic action heroine in a sequel that still has resonance today, courtesy of James Cameron. Lastly, The Aliens and Predators did eventually officially meet and fight the Terminators in the Alien vs Predator vs The Terminator comic series.
Genius Bonus: The primary location for the first two movies is stated to be located around the Zeta Reticuli star system. This little background detail becomes greatly more ominous when you know it is considered to be a potential place of origin of The Greys in UFO lore.
I Am Not Shazam: The term "xenomorph" was originally just intended as a throwaway and deliberately cumbersome term for a generic alien life form, like the taxonomic equivalent of "UFO" (it literally means "foreign or alien form" in Greek). It was never intended as the name of the species itself; only to show up Gorman for being an officious twat. However, the name has proved easier for fans to use than "the aliens from Alien," and it's consequently been used in official marketing materials and semi-canon sources.
Iron Woobie: Ellen Ripley. In the first film, she's the sole survivor against a creature which killed her shipmates. In the second film, she gets demoted for destroying her ship in her attempt to destroy the creature, and in the extended cut, we learn her daughter grew up and died during her overextended time in cryo-sleep. When she's called back by her company to investigate the colony on the planet from the first film, she finds another Iron Woobie in Rebecca "Newt" Jorden, the sole child survivor of the colony's infestation. Ripley, Newt, Marine Cpl. Hicks, and the android Bishop are the only ones to survive and escape the Alien-infested colony, only for Ripley to be once again the sole survivor after they crash-land onto a prison planet in the third film; and having been impregnated with a Queen chestburster in that grim setting, her only option left is suicide.
It's the Same, Now It Sucks!: As the franchise has progressed, audiences and critics have complained that the plots of the films tend to follow the same formula; a group of Developing Doomed Characters happen across a clutch of Xenomorph eggs in the aftermath of a massacre, all hell breaks loose, and there's a final battle aboard a spaceship with the threat of being sucked into the vaccum of space; and the whole plot is caused because Weyland-Yutani yet again want to try and weaponise the Xenomorphs. Even Alien: Romulus, a surprise hit and the highest rated/most financially successful film in the franchise since Aliens, was criticized for playing it safe and (for the most part) simply recycling the horrors of the original films beat for beat without really changing them. This trope may be justified because the horror of the setting comes from most people not knowing about the Xenomorphs, so every time a group of characters encounters them for the first time, they end up making the same mistakes.
Love to Hate: The Weyland-Yutani Corporation is so over the top in their ambitions and the unethical lengths they'll go to realize them, that it almost comes across as a parody. The overconfidence of the higher-ups in their ability to harness the traits of the Xenomorphs and them being oblivious to how out of their depth they are with this species adds to their ridiculous hubris.
The Alien series has a number of famous quotes that are frequently used outside of the film's context. They can be found on the films' YMMV pages.
On the receiving end of a number of memes making light of the fact that the franchise is now owned by Disney, such as showing xenomorphs at Animal Kingdom or depicting the Alien Queen or Ripley as Disney Princesses — or, in the Alien Queen's case, a Disney Queen, which would make all the rank-and-file xenomorphs into Disney Princesses.
Misaimed Merchandising: The Alien is one of the creepiest, most disturbing and most sexual monsters ever invented and most of the films of the series contain enough gore and horror to scar some kids for life. Yet, it hasn't stopped them from being merchandised, both as toys AND plush aliens and chestburster aliens. The Kenner toyline had such variations as Bull, Mantis, Crab and Jaguar aliens, making it one of the few toylines based distinctly around Bizarre Alien Biology.
Narm Charm: There were plans, believe it or not, to make a kid's cartoon about Aliens vs Predator. While it never went through, parts of it did make it into a comic book series made for the Kenner action figures, which had Ripley and most of the marines from the second film surviving Acheron, and subsequently going on GI-Joe style missions to battle Aliens throughout the galaxy, wearing brightly colored uniforms, sprouting endless one-liners note "HUG THIS!" and wielding goofy, cartoonish weapons (Ripley wields up a flamethrower that's bigger than she is). One Predator even appears to be wearing nipple cannons. When compared to the dark and gritty terror of the film, the whole series is hilarious.
Sequelitis: Notably avoided by Aliens, a great sequel which is widely considered to be as good as the first film. The third and fourth installments, and especially the AvP films, however, are considered a major step down. This is largely explained by the reasoning why the films were made. James Cameron was a fan of the original Alien and wrote the script to Aliens on spec. He was told that if The Terminator was successful he'd be allowed to direct the sequel he wanted to create, making it a labor of love. By Alien 3, however, the producers (who had meddled with the script of the first film) were making a sequel for the sake of the franchise. As such they burned through a bunch of different scripts and ended up with an amalgam of different attempts. Things didn't get any better from there. A number of people view that Resurrection might have been a pretty good film (a beloved screenwriter and a notable director with a solid grasp of visual style and atmosphere) if it hadn't been shoehorned into the Alien universe.
Viewer Gender Confusion: The Aliens themselves, especially the Queen who is often called a "she" in the films. Technically, all members of the species are or can be considered hermaphrodites (i.e. having both male and female sex organs) from a visual viewpoint, because H.R. Giger's design is neither male nor female but a disturbing combination of both sexes. From a reproductive viewpoint, the series tends to flip-flop between the Aliens being actual hermaphrodites (Giger's own original portrayal of the creature included human-like sexual organs, a scene deleted from the first movie had the alien being able to "convert" two humans into huge eggs with fully-grown aliens developing inside, the original design for the Newborn from Resurrection was that it was, like Giger's original model, possessed of a human-like vagina and penis) and the Aliens being asexual "drones" where selected individuals can mutate into/be hatched as parthenogenetically fertile female "queens".