When a character is a Jerk Jock, Alpha Bitch, or member of the Girl Posse they'll likely be beautiful, rich, and to some extent charismatic enough to be envied by the whole school. One thing they aren't likely to be, though, is smart. They rarely seem to suffer the ill effects of this as they are either:
Seen as too important to the school's sports team of choice (usually American Football) so teachers let them slide or assign them "tutors" who are in fact there to do their homework for them.
Because Daddy is on the board of governors of the school, that or he pulls out his credit card and gives the school a new swimming pool if they promise to let his little angel get A's.
Unlike Dumb Is Good, this is an example of the dim bulbs on a show being the mean ones. The exception to this is when the cool kids are seen as nice, where if this trope is in play they'll become The Ditz, or The Brainless Beauty (though a mean popular kid could be a Brainless Beauty too). This is a trope that rarely shows up in anime, because in anime the popular kids tend to be intelligent, unrealistically beautiful, aloof and wouldn't be popular in the real life Western World.
It has been noted that generally, popular people actualy have an about average amount of intellegence in their population as any group of people. Some are blindingly stupid, but some are actually smart. It also should be noted that generally, while some popular people are cruel and exclusive, some actually are nice people. (One wonders how a total bitch/bastard would get to be popular.)
When this is subverted or averted though expect the antagonist to our Cool Loser or Hollywood Homely hero to be much, much more dangerous.
This trope demonstrates the key difference between "knowledge" and "intelligence". Poppy McPopular doesn't know who René Descartes is or how to factor an equation because he skips class and doesn't pay attention even when he's there; this is not information he'll come by in his everyday life otherwise, and he doesn't consider it important. That doesn't mean he still isn't a brilliant strategist or leader; sports team captains are expected to memorize complicated strategies and lead their team effectively, things that require mental skills. Caring about science and math isn't seen as important in his worldview, and it's not the kind of thing that can be learned without effort, no matter how intelligent someone is. See also Book Dumb.
A particularly common trope in movies and television shows made during the 80's and early/mid 90's. It still crops up from time to time but with much less frequency than before due to such cultural changes as the mainstream acceptance of nerd culture and the dawning of the digital age.
See also: Alpha Bitch, The Cheerleader, Jerk Jock, The Ditz, The Brainless Beauty. This is often the cause of Future Loser. The counter part of this tropes is Intelligence Equals Isolation. These two tropes often coexist in the same universe because they hinge on the same principle.
Not to be confused with It's Popular, Now It Sucks.
Anime and Manga
Loveless: Someone researching Ritsuka's backstory discovered he used to be popular and got poor grades. Thanks to various events, including the death of his brother, he became anti-social and introverted, not to mention that his mother's already present abuse escalated.
Played straight in Clueless... kind of. Popular girl Cher is certainly not a genius-level intellect, but while she's a bit ditzy and naive in many ways she can also be surprisingly savvy, quick-witted and shrewd when she needs to be, being quite capable of "negotiating" her grades with her teachers.
Mean Girls. None of the Plastics (the clique of the most popular girls in the school) seem overly intelligent, with Karen in particular being an outright airhead. Even Regina, the arrogant and ultra-powerful Alpha Bitch, turns out to be pretty easy to manipulate (though calling her "dumb" as such is probably going too far, and once she realises what is going on she has a trick or two of her own up her sleeve).
Brad Bramish, the Jerk Jock of Brick, is a definite example. Laura, from the same film, subverts it.
Sabrina's college roommate Morgan is a good example, being both tremendously dim and very popular.
Pretty much every Disney Channel show ever to have a popular girl for a villain will make her seem dumb.
Subverted in Buffy the Vampire Slayer, where Cordelia proves to actually be intelligent (at least she tests well) and has a rather acute detective sense. All this is covered up by her "no reason for secrets" mentality and her self-centered priorities (with a hint of outright ditziness for flavor). In the original movie, Buffy herself was a subversion.
Cordelia's follower Harmony on the other hand is genuinely dumb.
Another funny aversion of the trope is the episode Doppelgangland, where Willow is asked to "tutor" one of the jocks. After running across Vampire Willow, he decides to do his homework himself.
Holly Fischer from The O.C. (especially in her later appearances when she is leader of a pack of young brides and very much the stereotypical Brainless Beauty). To a lesser extent Luke Ward, though he was a bit deeper than the usual Jerk Jock. Summer Roberts very much fitted this trope at the start of the series, but evolved into more of a Genius Ditz as the show progressed.
Subverted in Heroes. Claire is very popular at school, but she's also quiet, thoughtful and complex, and smarter than she pretends to be.
Initially played straight on Malcolm in the Middle—the normal kids keep several metres away from the gifted kids at all times, and the most popular kids aren't all that bright. A later episode subverted this when Malcolm met a another gifted boy who was the most popular person in his school and was invited to several parties a week. Also, as time went on, Reese, the stupidest boy in the school, ended up even less popular than Malcolm.
Got subverted in another episode, when Malcolm started dating a popular girl whose biggest secret was that she was quite smart and actually enjoyed studying. However played straight as the main reason she acts like an Air Head is to stay with the popular crowd.
In series 3 of The Mighty Boosh Vince Noir, the "Prince of Camden", arguably falls into this category at times.
El Goonish Shive both used and averted it, with the Jerk Jock fitting it (although not necessarily shown to be Book Dumb it takes a special kind of idiot to keep on bullying someone with a stronger, ki-using martial artist friend who has beaten him up several times in the past) while the Alpha Bitch of the other school has proved herself intelligent and observant.
Subverted in Penny and Aggie. Turns out Penny is just as smart as Aggie—giving Aggie another reason to hate her, since she doesn't use her influence in the way Aggie thinks she should.
Weregeek has Jess, the main character's non-geeky girlfriend. Jess herself is an aversion, but all of her other friends come across as vapid and clueless.
Solange, of the Whateley Universe. On the other hand, Kodiak, the new head of the Alphas, is turning out to be a lot smarter than anyone thought.
Dash, Kwan, and Paulina from Danny Phantom; Valerie, who was kicked out of the "popular" gang when her family lost all their money, has since shown herself to be of more-or-less average intellect for the Danny Phantom universe.
Kim Possible is a subversion, as she is both the smartest and most popular girl in school. Her rival Bonnie seems to be a close second in popularity, but although she is clearly not as intelligent as Kim, neither is she particularly dumb.
The Fashion Club along with Kevin and Brittney from Daria are perfect examples.
This becomes a plot point in the movies and in later seasons for Quinn and Stacy (to a lesser extent), as it is established that they are much smarter than they behave normally and dumb themselves down in order to fit in better.
This is also subverted by Jodie Landon and Mack Mackenzie; the former is most likely the most popular girl in Lawndale High and the latter is the captain of the football team, and they're two of the smartest and most well-adjusted characters in the series. Played much straighter with Brittany and Kevin, though. Though even Brittany shows alarming tactical knowledge and scheming ability when the situation calls for it or she's sufficiantly provoked.
Sym-Bionic Titan: Kimmy actually believed this trope to be true, as since she was popular she could never be smart. It wasn't until Newton showed her that she can pull off anything she sets her mind to that she subverted this trope.
Biology teacher: I'm not sure you understand. We want your grade to go up, not down.
An episode of The Replacements had Riley and Tasumi realize that guys fall head over heels for utterly stupid girls. They spend the episode trying to out-dumb one another, competing for the boys' attention.
In The Simpsons episode "Bart of Darkness", the family gets a pool and Lisa instantly becomes popular; when her brain points out that they're just using her, she delivers the page quote. At the end of the episode, the kids abandon Lisa because Martin built an even larger pool, leaving her stranded at the bottom of a now-empty pool.
Lisa: Huh? Hello? Hey, I'm stuck in here! I gotta think of a way to get out.
Lisa's Brain: Well, well, well; look who's come crawling back.