Totally Spies!/WMG

The world of Totally Spies is a future utopia
WOOHP is not a secret intelligence agency, it's a unified world government. It's been established that they have an office complex in at least most major cities, and they're physically connected to nearly every building (as seen each time Jerry summons the girls). It is evident that the girls do not practice espionage, as they have never been strictly required to disguise their identities; they're more like a body of crisis control or SpecOps that battles crimes too specific, grand-scale, or technologically-inclined for the regular police.

The crime comes about due to the easy availability of sophisticated technology. Education seems much more widespread and there doesn't seem to be a soul in the world beneath upper-middle-class, a time-honored trait of Sci-Fi utopias; high-tech devices like robots and hovering vehicles seem relatively common, as no one bats an eye at them, the space program is decades beyond our time, there is a heavy emphasis on cleanliness and environmental protection ("Even the dirt is clean!"), there are no overweight people, implying more health awareness and / or better health care, and a recent episode revealed that the animals at Malibu Zoo have been replaced with robotic replicas, indicating a leap in animal rights. To say nothing of the surprising Type One portrayal of Eagle Land, in a French production no less.

Of course, the dominoes are all set for a totalitarian government to usurp WOOHP. Given the organization's resources (if it has wires or runs on electricity, WOOHP has bugged it in some way), it'd be incredibly easy for a despot to monitor every aspect of the citizens' lives and turn the technology against its users. Jerry's utter inability to judge a person's moral compass, given the amount of transparently evil persons who have fooled him into trusting them, this seems eerily likely.

This subtext is all a hair away from text, though. To dive a little deeper...

The girls (and some of the villains) are vestiges of an old, failed Super Soldier program
It's no secret that the girls have a special gene that makes them more adept agents for WOOHP than the average person. But, if you'll notice, none of their gadgets seem substantially more advanced, technologically speaking, than the kind of consumer products you can buy (or even build) here. You'll also notice that few, if any, of the villains the "spies" are sent to defeat have political aspirations in mind; all of them are following some wild, nonsensical pipe dream for little more than personal fulfillment. Exhibit #3 is the apparent obsolescence of war. James Bond always had to defuse evil schemes that would result in explosive international incidents. The girls have never needed to bother with such consequences.

Now here is the juicy bit...

We can deduce, then, that the series is set long in the aftermath of an attempted War to End All Wars, using super soldiers. It was discovered, however, that although these soldiers were incredibly adept at strategic thinking and handling tech and weaponry, a large percentage of them were prone to long bouts of insanity and extremely skewed prioritizing (how else do you explain a maniac who wants to physically destroy the Earth because his pants fell off in public once, or one who wants to brainwash the entire world because they don't appreciate his performance art enough?). In light of the huge threat entire armies of these people represented, all world governments had to unite into a World Order of Human Protection, WOOHP, to keep the people safe.

Decades later, their goal is to isolate all descendants of the super soldiers who carried the defective gene from the rest of the citizenry... with the aid of those who turned out right.

This also explains why Sam, Alex, and Clover required no training, and why everyone they ever fight can hold their own against them, at least for a while.

All of the villains are killed by Light Yagami
The reason why all of the villains didn't appear after they were captured is because Light has killed them with his Death Note. An example is when Shirley, the spies' evil yoga teacher in Power Yoga Much, is arrested by WHOOP and never appears in the next episode. Why? Because he killed her by putting her name in the note, giving her a heart attack.

With this, the spies are able to have a peaceful world without knowing that Light has killed the villains they locked up.

Mandy is a distant descendant of Elmer Fudd
Really! Listen to them laugh!
 * I think she's related to Fran.
 * I love you.
 * Uh, thank you!
 * You're welcome. I should write a fanfic about this.
 * Let me know if you're done.
 * Somebody hijacked my joke with a much funnier joke. How very embarrassing.
 * Don't be! :D

All three of the main characters are super-slutty lesbians.
All that fanservice? Intentional.
 * The fanservice is obviously intentional, but the actual Wild Mass Guess here is asinine. There could not possibly be more evidence to the contrary.
 * Which its why it's  wild  mass guessing.

All three of the main characters are prudish closeted lesbians.
All those guys they seem to be interested in? Beards.
 * The episode when they go into the future the three of them are still living together

Sam has a Split Personality
It happens when she is Brainwashed and Crazy.

Clover's dad is Duke from GI Joe, and Mandy's dad is Cobra Commander!
Which is why they hate each other so much.
 * COBRAAAAAAA!!!

The villains that the Spies believe themselves to be facing are actually other WOOHP agents training them to go up against genuine threats; what's more, Clover is in on the deception.
Given that actual terrorists wouldn't have the bizarre hang-ups that the colorful assemblage of rogues we see on the series do, it makes sense that WOOHP is conducting a series of field exercises to train Sam and Alex to handle genuine menaces to society; Jerry knows that the process is a good one because he and his cyborg buddy Gadget used it to train the person Sam and Alex know as Clover.
 * This would explain how he always knows exactly what gadgets to give them...