Submitted: I'm starting to get into Greek mythology and I has wondering if you could do an article on how nymphs went from "divine protectors of the forests and rivers" to "OMG Beautiful Nymphs" in bad pop culture.
Sure, although there are a lot of layers going on with nymphs in both Greek mythology and popular culture!
One of the Aurea (nymphs of gentle breezes)
"Nymphai" is basically a catch-all term in Greek mythology for lesser nature spirits, all female, who are associated with various natural features and places. There are tons of more specific categories within the nymphai; dryades (lowland tree spirits), oreiades (mountain spirits), naiades (river and lake spirits), and nereides (ocean spirits) are all broad categories of nymphs. And then those specify down as well - a single naiad might be more specifically a heleaionad (a marsh spirit), a krenaiad (a fountain spirit), a limnad (a lake spirit), a pegaiad (a spring spirit), or a potamaiad (a river or stream spirit). And then those nymphai would be even more specific, because they were generally tied to a specific location as its inhabiter, so a single pegaiad is not only associated exclusively with springs, but with one spring, which would be her home and domain. There are some classes of nymphai that aren't tied to a specific location - the Maenides, Dionysos' handmaidens, are an obvious choices, as well as the nymphai that accompany Artemis on her hunts and the nymphai of the underworld or the stars that sometimes leave their home bases and travel in myth.
Local nymphai were generally considered to be worthy of respect and best not annoyed; while they weren't feared the way major gods were, it's just good sense not to piss off the nymph who lives in the local spring you get your water from, lest the water dry up or be undrinkable or bad things happen to you when you visit over there every day. Many nymphai were also considered to be related to the greater gods, so you also didn't want to wreck their home bases or aggravate them personally for fear they might have important relatives; for example, all of the Nereids were considered the daughters of Nereos, god of the Aegean Sea, and handmaidens to Poseidon, so bothering them was not a good idea unless you wanted to risk sea monster problems on a grand scale.
Most of this plays into the Ancient Greek idea that humanity needs to be careful to interact with the divine in a respectful way lest they fall prey to the sin of hubris and be punished; casually disrespecting or defacing a tree might in turn anger a dryad associated with it, which might in turn result in small local problems (no more useful growth in the area of that tree, dangerous accidents around it) or much bigger ones (the dryad's uncle, Ares, takes personal exception to your harassment of his niece and about the only good news is that you really don't have to worry about whether you're going to need to wear a helmet to harvest apples anymore). Every tree might or might not have a dryad, every hill an oread, every small stream a naiad, and so human beings needed to respect nature and its useful features even while they used them, or face the consequences.
Achilles is a lot of things, but foolish enough to annoy this nereid is not one of them
So how do we get to pop culture depictions of nymphs as buxom, sex-obsessed bubbleheads who spend all day frolicking in fields and banging every eligible dude who comes their way? Sadly, the answer is pretty much just old-fashioned garden-variety (ha) misogyny, by way of nineteenth century European revisionism.
Nymphai, as we said up above, are all exclusively female; in fact, most lesser deities and spirits in Greek mythology are considered female, even with the occasional orders of male spirits like the satyroi or the oneroi representing more masculine types of divine power and the occasional orders of spirits that aren't marked by gender or are considered fluid. Because they're divine, but not too divine, they're also convenient figures as parents or love interests in myth, so there are quite a few stories in which they are the parents of heroes or have extramarital affairs with the major gods in order to give birth to minor deities who feature in other stories. For example, Thetis, leader of the nereides, is the mother of Achilles and a massive temptation to Zeus, and there are plenty of stories of nymphs being pursued by the gods (who don't always catch them; just look at Minthe, turned into a plant by Persephone to prevent Hades from catching her, or Daphne, who transformed herself rather than fall prey to Apollo).
Now, in the eighteenth century, northern Europe ran full-tilt into the Enlightenment, which involved a lot of philosophical change and study that is too much to go into here, but it also carried on the tradition started during the Renaissance of Europeans getting very interested in classical mythology. It was extremely in vogue to learn ancient Greek mythology, read the ancient Greek philosophers, and discuss how modern Europeans were clearly the spiritual and cultural inheritors of ancient Greece. Everyone wanted to claim how modern Europeans were the rightful heirs of all the brilliant art and incredible engineering and advancements of ancient Greece, and therefore tons of new writing and art happened; this is where we get all those paintings of ancient Greek mythological scenes starring whomever the painter's current clearly not-Greek patron was, and where we get all those retold-for-later-audiences versions of myths, often with very weird additions based on whether or not the myth's Greek moral needed to be converted into a British or German or French one. We still deal with a lot of mythological study being based on writing from this time period and as a result having a lot of weird biases baked into it.
Water Nymph, Gaston Brussiere, 1899
And that's where the perception of the nymphai comes into play. To European scholars of the time, the nymphai read as simultaneously laudable and scandalous. They represented innocence and goodness by being pastoral representatives of the natural world (pastoral representations of the natural world were VERY in; everybody was about getting back to nature and throwing off the shackles of modern humanity's ethics and progress because the Industrial Revolution was super gross and stressful, etc.), and therefore they were often the subject of poetry and art that depicted them as carefree, beautiful beings who romped about in nature, and who had a lot of sex because that was what natural creatures like animals did (it didn't hurt that they were often associated with the satyroi, who were already depicted with tails or other animal characteristics). In these cases, depicting nymphai as being very sexual was a way of illustrating them as just another part of nature, where sex was a normal thing that happened all the time and was free of human moral issues surrounding it.
But, on the other hand, the nymphai were also representatives of licentiousness and wanton feminine wiles and general Bad Things to the same mostly white, male, and Christianly uptight writers. As mothers of various heroes, lovers of various gods, and sometimes appearing in explicitly sexual roles (like the Maenides, for example), they were also representatives of dangerous feminine sexuality - constantly naked (though ironically this is only in intentionally pornographic ancient Greek art; in regular art, nymphai were usually depicted fully clothed, and the stereotype of nymphai being nude all the time is also something European painters did in their quest to depict them as part of the natural world), super alluring, having sex with people they weren't married to (or even in defiance of their partners' legitimate marriages!), and being pursued by even more people that clearly wanted to have sex with them, the subtext there being that this was clearly the fault of their lady-wiles. (A moment of silence for poor Apollo/Zeus/Hades/Poseidon/everyone else on the list who was clearly an innocent victim of Overwhelming Lady-Wiles.)
As a result, they were also easy targets for moralizing about inappropriate sexiness, and the perception of them as unreasonably sexy and without morals led to the word "nymph" being associated with the concept of a lascivious woman, and eventually to being cemented by the invention of the term "nymphomania" in the late eighteenth century to describe a woman who suffered from clinical hypersexuality (although let's be real, many women at the time who were diagnosed with the disorder were really just being diagnosed with "wants to have sex even though not married", "wants to have sex even though barren so what's the point", "wants to have sex more than husband and he's weirded out about it", or "had sex with someone OTHER than husband, to the asylum").
Nymphes et Satyres, William-Adolphe Bouguereau, 1873
Even though the field of psychology doesn't use the term nymphomania anymore (or satyriasis, which was the same diagnosis for men), "nymphomaniac" survived as a colloquial term for women who have or want too much sex, and modern pop culture tends to represent the nymphai, when they occasionally appear, as a combination of those two old eighteenth- and nineteenth-century concepts. Add "childlike innocent in nature" to "hypersexualized woman having all the inappropriate sex", and you end up with our stock trope for nymphs: "childlike or extremely stupid woman who will have sex with everyone". The most egregious example of this I can think of is in Piers Anthony's Xanth series, where nymphs are represented as empty-headed not-quite-people who want to have sex with every man they see, but you'll see it in other places, too, with the recurring image of a nymph as a beautiful, none-too-bright-or-important lesser spirit who is just around to amuse the audience or occasionally represent A Dangerous Temptation to a hero.
Personally, I'd love to see more modern depictions of the nymphai in their original guise as the representatives of the natural world and the small powers that made up the first level of interaction between humanity and the much loftier, more distant gods. Respect your local epimeliades, y'all - without them, we wouldn't have apple cider!