Aerith and Bob: The Twins were renamed to Areekareeyuket and Bob for the series. During a Christmas episode, the first's name was actually written as a series of mathematical concepts on his Christmas stocking, while the second one was simply written as "BOB".
Affirmative Action Legacy: Agent X is an in-universe example. He's unprecedented in the series, as he's an MIB field agent who's - well - an alien. Zed was previously against alien agents (due to their unfamiliarity with Earth's norms and the potential for exposure), but he was pressured into it to calm down alien rights advocates.
Alternate Continuity: L still works for the MiB (and had been there for a longer time than J, apparently) and is a blonde. K wasn't neuralyzed or was, and got his memory restored as per the 2nd film.
And I Must Scream: Jeebs' race can consistently regenerate, but they need oxygen to do so. At the end of "The Blackguard Syndrome," J blasts Jeebs' brother before he gets sucked out into space. He gets better in "The Cold Sweat Syndrome," though.
Arbitrary Skepticism: Zed insists that monsters and ghosts and the like don't exist, while kids are being abducted by a walking Jack O'Lantern and HQ is experiencing a haunting. He's right; both occurrences are actually aliens.
Art Evolution: J and K got character redesigns after the first season. L became less pale. The Worms also got a lighter yellow color instead of the darker brown they started with.
Ascended Extra: Jeebs, Frank and the Worms. Essentially one scene wonders in the first movie, but with frequent appearances in the series (each even scoring major episode plotlines to varying degrees). Their status as AscendedExtras on the show led to their becoming AscendedExtras in the next two movies.
Back-to-Back Badasses: In the Season 3 "The Put Out To Pasture Syndrome" where Jay and Zed are facing against Alpha's mirages.
Bad Future: "The Future's So Bright Syndrome," where a tyrannical Worm has conquered Earth and is overseeing the extermination of the human race.
Batman Cold Open: Almost every episode opened with J and K on a mission unrelated to the main plot.
Also one from "J" in "The Big Sleep Syndrome" when L sacrifices herself by getting shot by J's gun held by the alien in J's dream, in order to force J to snap out of it.
Body Horror: Alpha steals alien body parts and integrates them with his own. His first appearance no less has him stealing a Sintillian heart. With each appearance, Alpha himself would look less and less human.
Celebrity Paradox: In "The Star System Syndrome," an agent proclaims "We've got Will Smith, Tommy Lee Jones and Rip Torn." Later in the episode, the Worms disguise themselves as a Mr. (Lowell) Cunningham and wind up pitching a movie about "well-dressed men and women" who police "bad aliens" on Earth.
K: Now we have to neuralize all of Hollywood. Again.
J: So that's why they keep making the same movies over and over!
Characterization Marches On: The Arquillians are established as pacifists in the series, whereas in the first film, they were willing to destroy Earth in order to stop the Bug from getting their galaxy if the MIB failed to get it back.
The Chew Toy: Jeebs. Every time he appears, count on a body part needing to be re-grown.
Clone Degeneration: The Quick Clones have a time limit. Once they run out of juice (or if you press the button behind their ear), they start babbling gibberish and quickly dissolve into coffee-colored gunk.
Clothing Damage: "The Hots for Jay Syndrome" to J, twice. Having fire sprout from your skin tends to do that. The first time they quickly got him some heat-resistant clothing, but falling to Earth from orbit overwhelmed even that.
Cursed with Awesome: J was in a hurry to lose his agility superpowers for no conceivable reason.
Cyborg: In the last season, Alpha makes himself one of these - reasoning that flesh ultimately decays.
Dawson Casting: "The Back to School Syndrome" has J go undercover as a high school student.
E.T. Gave Us Wi-Fi: A plot point in several episodes where advanced alien technology humans won't be ready for until several decades/centuries causes serious trouble, most notably the Cosmic Integrator that allows Alpha to chop up alien parts and tack them onto himself. It is also implied that some familiar technologies, including the 8-track tape and the Clapper, were alien inventions.
Everything's Better With Bob: Said half of The Twins. And he's a certified pilot, too.
Fantastic Racism: Pretty much the bedrock of a lot of the alien conflicts in the series, most notably the Fmecks and their obsession with wiping out the Arquillians. A rare human example is Edmund Clark Moffet, a paranoid alien conspiracy theorist who sought to erase MiB from existence to keep aliens off Earth.
15 Minutes of Fame: Agent X called for a tv crew from his home planet so they'd make him the star of their show. Being unable to get rid of them, Zed punished X by offering a chance to have K instead of X as the star, which they quickly accepted. As J pointed out, fame was so fickle X didn't even had fifteen minutes of it.
Flanderization: The worms and their obsession with coffee, though it helps that the reason for that obsession is also explained (on their planet, only royalty is allowed to drink it).
J also gets hit hard. The series stuck with the "new, inexperienced agent" role from the first movie, but J basically never grew out of it. There was a total of one episode where he seemed to actually become competent, which was forgotten by the next.
For Halloween, I Am Going as Myself: Or as a completely different alien species. Additionally, a good chunk of monsters in movies are actually alien actors in their birthday suits.
Good Thing You Can Heal: Jeebs provides this, as his race can regenerate from nearly anything (even being reduced to gelatinous goo!) as long as oxygen is available, though he can still survive just fine even if there isn't.
Groin Attack: L does this to a bug. "Soft underbelly," indeed.
Guns Are Worthless: It's a wonder J even carries the Cricket at all considering the number of times it's simply knocked out of his hand. This hold true for other agents as well. Ironically, Jay gave his cricket a silencer to stop the recoil.
Halloween Episode: "The Jack O'Lantern Syndrome," where Jay and the trick-or-treating Worms encounter a being preying on children, while spooky occurrences plague MIB headquarters.
Hero of Another Story: In "The Opening Gambit Syndrome," the reason why the Ixions didn't invade thirty years earlier. Alpha struck a deal with Vengiss to get the Ixions Earth's oil deposits in exchange for him getting control of Earth. However, plans changed because of Zed. He had been investigating Vengiss' presence on Earth and was about to crack everything wide open. If he had, Alpha knew MIB would defeat the Ixions - thus prompting a delay until the organization's guard would be down.
Hive Mind: In the series the Bugs are an insectoid Hive Mind species, which the writers probably used as justification for having every male Bug played by Vincent D'Onofrio.
J: You can't just operate on people without their permission!
Zeeltor: I'm pretty sure I can. I do it all the time.
Mattress Tag Gag: One episode features an alien race that's downright obsessive about law and order, complete with an ultra-brutal gulag for housing the many, many lawbreakers they round up. How strict are they? When Jay finds himself in the prison, he asks a fellow inmate what he's in for, and, well, it turns out they take their mattress tags very seriously.
Mugging the Monster: In "The Back to School Syndrome," a pair of Jerk Jocks take to bullying an undercover J. They turn out to be aliens, but they're unaware that J is MIB.
Must Have Caffeine: The Worms in MIB absolutely love it — apparently coffee is a drink reserved for royalty on their home planet.
Mythology Gag: One episode shows an in-universe Men In Black movie, with Agents Smith & Jones more closely resembling Will Smith and Tommy Lee Jones than the cartoon's character designs. Earlier in the episode, a movie producer was talking about getting Will Smith, Tommy Lee Jones, and Rip Torn for a film.
In "The "J" is for James Syndrome," the neuralyzed J is made an agent again. What follows is a montage of putting on the suit, followed by:
J: Y'know the difference between you and me? K: You make this look good. J: How'd you know I was gonna say that?
In "The Breaking News Syndrome," Zed summarizes MIB's mission as to "protect the Earth from the scum of the universe" (quoting the movie's tagline).
The Needless: It's revealed that Jeebs (whose species can regenerate from being blown to pieces) and his Psycho for Hire brother don't need to eat. Then the former brags that they don't even need to breathe oxygen to live, only to regenerate. Since they're in space at the time, J promptly opens the airlock and shoots said brother.
Out Of Order: "The Musical Chairs Syndrome" was the fifth produced episode in Season 4, but was aired first. It shows L being made a field agent. Consequently, "The Future's So Bright Syndrome" was produced first and features L explicitly asking Zed for a transfer to field agent.
Inverted example: "The Zero to Superhero Syndrome" was produced second in Season 4, but features Zeeltor before his introduction in "The Musical Chairs Syndrome." Fair enough, as the former was aired later in the season, but reruns air in production order, so yeah.
Reed Richards Is Useless: MIB is full of advanced technology that would effortlessly transform the world, but is largely kept under lock and key...because Earth simply isn't ready. MIB examines each piece of technology carefully and selects an appropriate time (sometimes even centuries away) for when humans will be ready to handle it.
Ret Gone: What one villain tries to do to MIB's founding members and thus the organization.
Sealed Evil in a Can: "The Out To Pasture Syndrome" ends with Alpha becoming this, being incarcerated in a chamber at MIB headquarters. Agent J is tricked into releasing him in "The Opening Gambit Syndrome".
Shout Out: In "The Inanimate Syndrome", an alien that can turn itself into any inanimate object tries to hide as a mannequin. The mannequin's head gets knocked off and proceeds to sprout spider legs and crawl away.
Sibling Rivalry: All Bugs are the offspring of their Queen, and in "The Big Bad Bug Syndrome", they squabble over the bounty on L for killing Edgar.
Spare Body Parts: Sintillians have two hearts, and are functionally immortal so long as both are working and "no-one drops a piano on them". K makes it clear to J that this doesn't make the Organ Theft any better. "You have ten toes. You woke up with one missing, how would you feel?"
Spotlight-Stealing Squad: Practically every episode in the later seasons featured a Worms subplot, if they weren't involved in the main plot.
Surrounded by Idiots: Zed has this attitude in several episodes, most notably the Halloween episode.
Surprise Checkmate: In "The Opening Gambit Syndrome", J tries to get information out of the imprisoned Alpha by offering to play chess with him. He's checkmated twice by the same distraction tactic. After Alpha escapes, he applies the same tactic to reality - this time, J sees it coming.
Take That: The end of "The Star System Syndrome" sees Hollywood making a rather accurate movie about the Men in Black.
K: We'll neuralize the town. Wouldn't be the first time. J: So that's why they keep making the same movie.
Frank the Pug claims he's way uglier than Cindy Crawford. Jay agrees that she's hideous and has to find out if Frank can live up to his claims.
The Unmasqued World: During the Grand Finale, an unmatched alien threat leads to MiB revealing the existence of aliens to the entire world, so that the entire planet can fight for survival. Then subverted, when the MiB are being honored by the American government, and J points out that everyone on Earth is watching the ceremony, so Z & K take the opportunity to neuralise the entire planet.
Who Even Needs A Brain: In one episode, Zed had his brain stolen. His body is able to keep functioning, albeit without any direction, because alien technology kept the two linked even at a distance. "Alpha has a sick sense of humor."
Who's on First?: Comes up whenever Agent U is needed. J got around it by figuring out U's real name, since there aren't that many names beginning with 'U' for men. Averted with K.
Who Would Be Stupid Enough: The alien race who are zealots about law and order, seen under Mattress Tag Gag above, J asks both K and the cop from the world they captured why anyone would go to this world when it has such strict policies, K and the cop reply in unison: "The beaches."
Wreathed in Flames: The episode "The Hots for Jay Syndrome" has Jay gaining fire powers after eating alien food. Surprisingly, this was actually treated like a bad thing. All that energy has to come from somewhere, and in Jay's case was being leeched from every cell of his body. It would have killed him if it hadn't been reversed.
You Hate What You Are: Alpha is a self-loathing human and has been forcibly grafting alien body parts onto himself in an effort to gradually remake himself as the ultimate Frankenstein monster of alien parts, and become functionally immortal. In one episode Alpha actually grumbles about how unhappy he is that he still has parts that are from his own "stupid" species.