Where on Earth Is Carmen Sandiego? provides examples of the following tropes:
Absurdly Spacious Sewer: Carmen leaves a clue in the Paris Sewers Museum for Zac and Ivy. And yes, it still reeks down there.
The Ace: Lee Jordan, initially. Despite having solved over a hundred cases in four years, capturing Carmen at one point in his career, and having saved Ivy's life in the most dramatic way possible, though, his poor treatment and disrespect towards Ivy (along with sabotaging the Pentagon's computer systems, forcing Zack to pull out of the case temporarily) and Carmen (when he starts working for her after defecting from Acme)deconstructs him into the Jerkass and muchworse.
Alternate Continuity: The Where on Earth...? arc is separate from the rest of the Carmen Sandiego series. The black-haired Carmen in this cartoon has not appeared in any other story; even in the Junior Detective computer game, her canon foes Zack and Ivy were chasing the original, brunette Carmen.
The Facebook game may possibly be the closest version to match Carmen's characterization from the cartoon, not only in described appearance (black hair, light-colored eyes), but also her Back Story as an orphan and aversion to violence.
Amazonian Beauty: Ivy gets mistaken for an Amazon in Ancient Rome after she effortlessly flips an armed centurion into a public bath with only her bare hands. She later proves she can hold her own in the Roman Coliseum.
Anti-Villain: Carmen, especially later in the series. In fact, she often gets to the point where the Anti-Hero label could even apply sometimes.
Call Back: When Zack tells Tatiana he could kiss her after solving one of Carmen's clues, she tells him, "I never kiss on the first case." Later in the series Lee Jordan says the exact same thing to Ivy, and Ivy shoots him down with the same exact words Tatiana said to Zack.
Another Call Back: After getting the history of the American Revolution back to normal in "A Date With Carmen: Part 2", Zack set down the Chronoskimmer just for a second — in which it gets swiped. In "Labyrinth: Part 1", Zack recalls the stolen Chronoskimmer and the Chief recalls his British accent from the first time travel incident.
Chekhov's Gun: The anti-crime sticky foam Carmen had stolen at the beginning in Deja Vu becomes this when the time came for Carmen to make her getaway. Interestingly enough, Suhara knew from the beginning the sticky foam didn't fit Carmen's MO in the episode, and prepared a Batman Gambit, but not without subjecting Zack to some Trickster Mentoring.
Digital Destruction: Eleven of the episodes included on the Complete Series DVD are encoded to play stretched to fill an HDTV when viewed with a Blu-ray player.
Doesn't Like Guns: Carmen and ACME. Carmen doesn't believe in brutal direct violence—relying entirely on skill and intellect. Carmen even chastises Lee and his men for using weaponry as their approach is more vicious. And ACME doesn't want their employees using guns of any kind. Well of course, they don't. They're all children!
Dressing as the Enemy: Zack and Ivy end up dressed as VILE henchmen a few times, and Ivy takes on the mantle of The Tigress to make Carmen jealous of a new thief in town.
Easily Forgiven: In one episode, Doctor Sara Bellum committed a series of violent and destructive crimes, disguised as Carmen, so that if her plans failed, Carmen would take the blame. In later episodes, we see Sara Bellum working WITH Carmen again, and no mention of her previous treachery is made.
Enemy Mine: A good chunk of the "Retribution" episodes. A minor example also happens in When It Rains.
Even Evil Has Standards: Carmen and Lee Jordan have a falling out over his unwillingness to play by her "rules", which included an attempt to murder Zack and Ivy by cutting them from a rope hanging high above the ocean.
Also Carmen's non-violent brand of thievery as contrasted with Maelstrom's and Sara Bellum's.
With Mason Dixon, Carmen's higher standards are those of intellect, as Dixon is a total moron.
Expy: Russian ACME agent Tatiana bears an unmistakable resemblance to Russian Planeteer Linka. They also share the same voice actor: Kath Soucie.
Face-Heel Turn: Carmen's Back Story, same as in the game canon. Ditto for Lee Jordan not long after he was introduced. Maelstrom was mentioned to have been a brilliant marine archaeologist before turning to a life of crime.
Faceless Goons: Any generic VILE henchman. Thugs wearing caps, goggles and uniforms.
Faking the Dead: In "Follow My Footprints", Carmen faked her own death and left a set of clues for her henchmen and Acme to solve. It was all to figure out who was worthy to be her successor . . . ironic that Zack and Ivy were the only ones to actually solve all three clues.
Family-Friendly Firearms: Most of the "weapons" shown are grappling guns or nets, with Lee Jordan's thugs using laser beams in the finale.
Featureless Protagonist: The player(s). We can see his skin, and get a vague notion of age (around 12 or so) and he appears to be white, but that's about it. Another is a black girl who seems slightly younger.
Some episodes had a dark-skinned girl as the player. We still never see a face, and ultimately know nothing of the player's personality other than having a solid determination to catch Carmen.
Full Name Ultimatum: Mild version, since Zack and Ivy don't seem to have last names - Zack is rarely called by his given name (Zachary) unless he's done something to royally piss off Ivy.
Fun with Acronyms: Back in Carmen's detective days, the Chief was better known as the Computerized Holographic Imaging Educational Facilitator.
Game Between Heirs: Carmen's will placed her main henchpeople and the main detectives on a scavenger hunt to decide who's fit to inherit her place as head of VILE. Zack and Ivy win, and we learn the whole thing was a Batman Gambit so Carmen could choose her heirs.
Genius Bruiser: Ivy is well read, and appreciative of the arts. She has also been seen to hurl various henchmen who tried to restrain her. Or chase her. Or escape her. Or try to whip her. And not just VILE's henchman.
Guest Star Party Member: Non-video game example (Fanon Dis Continuity notwithstanding). In some episodes, Ivy and Zack will request the assistance of other Acme detectives when they need help, other times the Chief will tell them who they'll be working with.
She manages to swipe Mona Lisa's smile and even tries to make off with the Statue of Liberty in the opening. And that's leaving out the things she swiped in her first time travel heist that changed history, or technology to steal musical talent!
And yet she tops herself in "By a Whisker" when she steals a beach (Kaimu Beach in Hawaii)which she planned to use as a huge litter box for two white lion cubs. Ivy's response? "The entire beach?!"
Inside a Computer System: The C5 malfunctions due to Carmen's interference, dumping Zack and Ivy inside the Acme Mainframe.
Jerkass: Lee Jordan—a star ACME detective, who later evolves into a complete sociopath.
Kick Chick: Ivy's preferred combat technique involves flying kicks. She's also kicked open doors bolted with heavy lumber by kicking them open, and her legs are apparently powerful enough that she once freed herself from a pillory. She's something of a black-belt.
Knight of Cerebus: Lee Jordan and Dr. Maelstrom, both far more dangerous adversaries than Carmen.
Latex Perfection: How Carmen pulls off her disguise as Marcus Aurelius in Labyrinth Part III. Unlike other examples it explains that she used a bust of him to pull it off.
Magical Computer: The Acme Mainframe can do damn near anything, including teleporting the detectives the whole way to the Moon at one point.
Magic Countdown: In "Follow My Footprints", Zack and Ivy have 60 seconds to catch Sarah Bellum on the Moon, and if the Chief missed with the C5 they'd all be stuck there. As the mainframe's going into its final countdown, the Chief pops up to have a Big Damn Heroes moment, but that takes longer than the 5 seconds remaining.
The Nineties: The show's internal chronology places the events of the series in the 1990s, when it was produced.
Nobody Here but Us Statues: Done in the Louvre Museum in the very first episode. Subverted when the guards spot them instantly and capture them, and Ivy berates Zack for coming up with such a stupid plan.
No Fourth Wall: The characters are not aware that they're characters on a TV show, but they are aware that they're characters in a computer game, and speak directly to the player often.
No Honor Among Thieves: Carmen gets betrayed by her henchmen no less than three times during Season 2 alone. And ACME hotshot Lee Jordan turns against everyone—going into business for himself and becoming especially mad-sadistic.
Not Herself: Zack and Ivy wonder if Carmen has lost her mind when some of her crimes border on pure destruction, especially with the theft of the Spruce Goose and torching the Amazon rainforest. They become even more suspicious with some of the clues they receive, saying it wasn't like Carmen to leave extremely easy clues. It was actually Sarah Bellum impersonating Carmen, during the midst of a Villainous Breakdown.
Noodle Incident: The first episode has Ivy tell the Player that she owes Carmen for a particularly humiliating defeat once, details of which or never given.
Not Me This Time: The only time that Ivy and Zack actually catch Carmen is when she didn't do what they caught her for.
Not So Different: Both Lee Jordan and Maelstrom tell Carmen that she is no better than them, despite her "lofty moral superiority." She proves Lee wrong on his charges, but Maelstrom isn't refuted on his.
Subverted in that Carmen never says this to Zack and Ivy, even though she considers them her successors.
One Steve Limit: Subverted. There are three characters who share the name Lee, the first one is Lee Jordan, the second is Lee Galease, and the last one a Guest Star Acme Detective who works in Macao. Granted, the Guest Star Detective's name could be spelled a variety of ways and might even be his surname, not his first name, but short of closed captioning, his name spelling remains unknown.
The latter was foreshadowed in a Season 1 episode. It also provides a Red Herring Twist subplot near the end of the series, where Carmen learns she might be the long-lost daughter of the wealthy industrialist she's stealing from.
Public Domain Soundtrack: Used "Singt dem grossen Bassa Lieder" by Mozart as the opening theme but with a more "modern" sound and obviously different lyrics. The ending theme was sometimes an instrumental version.
Punny Name: Good Lord, and how. Sara Bellum, Ace Bandage, Claire E. and Cora Net, Paige Turner, Phill M. Critic, Al Loy, every one of Carmen's henchmen who wasn't a Faceless Goon had a job-specific name.
The Real Remington Steele: Played with. Sir Nigel Fenwick, an inspector working for Scotland Yard, appears briefly in A Higher Calling, but Zack and Ivy don't actually meet him until much later in the series. Who they thought was Sir Nigel Fenwick in By a Whisker was actually Carmen's henchman Frank M. Poster impersonating him. They meet the real deal in Birds of a Feather
Recurring Dreams: Carmen suffers from nightmares in the episode "Shaman Spirits".
Ridiculously Human Robots: The Chief is effectively an Omniscient Database with an AI interface, but he's still capable of all the emotions a human is. Too much, some may say. As he's a hyperactive wisecracking scene-stealer.
Sci-Fi Writers Have No Sense of Scale: In one episode, Carmen decides to play the ultimate game of chess, and sets out to steal the appropriate pieces. She steals the floor of the Citadel in South Carolina (famous for it's red and white checkerboard pattern) for the board, and various statues for the pieces. However, what does she get for her rooks? Actual castle turrets that are way to big to fit on the gameboard (hell, the gameboard should have fit in the turrets.)
The Starscream: Sarah Bellum in "When It Rains" and Mason Dixon in "Timing Is Everything".
The Stinger: Each episode from the last season has an extra scene play during the end credits.
Stolen MacGuffin Reveal: The first episode ends in this. The reveal comes not from the fact Zack and Ivy recovered the stolen artwork, the reveal is that Ivy replaced whatever masterpiece Carmen had in mind from what basically amounted to vandalizing three priceless artworks with a picture of the detectives drawn in stick-figure form.
Tech Marches On and/or Magic Floppy Disk: The Acme Detective Agency's entire database, Chief AI and all, can supposedly fit on a single standard CD. Granted, it was one of Carmen's own pieces of tech that pulled it off but still, she effectively stole The Other Wiki and put it on a CD.
Teen Genius: Zack, and according to her backstory, Carmen.
This was lampshaded when the detectives travel to the future during Carmen's second time travel heist. After being dumped into yet another ridiculously precarious location, Zack complains that having been 100 years since they left, you'd think they could have worked out the kinks by now.
A Date With Carmen: Carmen swipes things from the American Revolution, and causes it to fail. The Chief turns British and the USA is still a colony. A little later on in that heist, she swipes Ben Franklin's key and takes out electricity (along with both time machines) until it's returned.
Timing Is Everything: Mason Dixon steals a ride in Carmen's time machine, and screws up the past to the point where Carmen's just a second-banana sidekick member of VILE with poor self-esteem. She even wears gray from thereonin like those of the South Confederate. And has a gray persona to match.
Tempting Fate: Happens every now and then. Zack is generally the instigator when it looks like things can't get any worse.
There Are No Therapists: This would explain why Carmen is talking to a hypnotist after the traumatic events of the series finale, instead of...you know...a shrink.
Thirteen Is Unlucky: Pretty much the plot of Curses, Foiled Again - everything in the episode takes place on Friday the 13th.
Time Machine: Two of them: the Chronoskimmer, which looks like a PDA or remote control and is used along with the C5, and Carmen's timepod, which looks like a more traditional time machine.
Title Drop: The Player drops the title of "Music to My Ears" in his end talking with Carmen Sandiego.
Tongue on the Flagpole: A variation; in one episode, Zack is saved from sliding off an icy rooftop when he gets his tongue caught on the gutter.
Translation Convention: Averted. Instead of everybody around the world speaking English, people in non-English-speaking countries actually speak their native language (often with subtitles). Fortunately, Zack knows a large-but-never-specified number of languages and can almost always translate.
Universal Driver's License: Played with in Zack's case, interestingly enough. He can barely drive the C-5 car, but seems to have no problems operating single (or double, at most) passenger hovercrafts and vehicles, even if it belongs to VILE.
Villain Exit Stage Left: Zack and Ivy always get to Carmen just in time to watch her escape, after which one of them says something like, "Maybe next time!" Yeah, right.
Villain Protagonist: Emphasized in the finale: Carmen has a heart of gold that she wears on her sleeve, Lee Jordan is sadistic and seemingly without any conscience at all.
Villainous Rescue: Carmen saves Zack and Ivy's bacon numerous times, but it especially applies to her defeat of Maelstrom and Lee Jordan.
Villains Out Shopping: Literal example in Moondreams, where Carmen and two of her henchpeople went to a toy store and actually paid for a toy. Subverted when the Chief mentions an uptick in VILE activity around the world and that Carmen was possibly planning something in the works.
When I Was Your Age: Carmen points out she didn't have all the fancy technology Zack and Ivy take for granted back when she was an Acme detective. The flashback in Retribution, Part 1 shows how justified she was.
In one episode, the player dares Carmen to try something without any of her high-tech equipment. She agrees to this, and actually pulls it off, hijacking the Orient Express with only conventional tools. But as Ivy suspected, Carmen is Genre Savvy enough to keep an escape craft around to flee after she's made her point.
Worthy Opponent: Carmen is sometimes depicted as genuinely liking Zack and Ivy, and enjoying the ongoing battle of wits she has with them.
Zack and Ivy seem to have some form of respect for Carmen as well, even letting her have a Mercy Lead in one episode.
Carmen and Malestrom, both in the past and in the present.
Xanatos Gambit: One episode has Carmen creating a huge diamond, which she then uses to scramble the laser that somehow runs ACME's main computer system, effectively shutting it down. Zack then reconfigures it so that, instead of scrambling the system, the diamond increases the computer's efficiency, letting them almost catch her. Toward the end, Ivy mentions that Carmen must have known that was a possibility, and she and Zack are left wondering if she did the whole thing to give herself more of a challenge.