There are several stereotypes that support the notion that beautiful women can't be intelligent, and intelligent women can't be beautiful.
I've always loved the old classic horror films, and a prevalent plot device in these films would pair a female "ice princess" scientist with a rough-and-tumble masculine hero. The other men in the film warn the hero to not attempt to approach her, that she is too cold and distant. The female scientist is always all business and no hanky-panky at the beginning of the film. Invariably at some point in the film the female scientist is saved from the monster by the rough-and-tumble hero, at which point she melts into his arms, and now coos warmly and affectionately at the man she formerly scorned. Science and protocol fly out the window as the two profess their love for each other and the monster dies by the final reel.
Another version of this stereotype is called the "Miss Jones Syndrome." where a seemingly unattractive, bespectacled woman is told to take off her glasses and loosen her hair, and voila! "Why, Miss Jones, you are beautiful."
There are many variations and parodies on this theme. In his music video "She Blinded Me With Science," Thomas Dolby did an homage to this Cliché with the line, "Good heavens, Miss Sakamoto, you're beautiful!"
Two recent films explore this theme, "10 Things I Hate About You," and "She's All That." Both stories revolve around female leads that are intelligent and witty. They are also considered unattractive, not so much because of their looks, but because of their independence and attitude. (Imagine that!) Their male suitors must tame them until they are brought under submission. This rather sexist storyline is actually a recycled version of "the Taming of the Shrew" by William Shakespeare.
Another recent film that portrays these stereotypes is the film, "Not Another Teen Movie." The film is a parody, and the female lead portrays many of the cliches mentioned. The title of the book the character is reading in the center still in the photo above is "How to get the Popular Boy Without Compromising Your Unique Rebelliousness."
Independent women are sometimes portrayed on television as lead characters, but usually the same or similar stereotypes apply. Dana Scully is portrayed as very intelligent and perceptive woman in the television show "The X-Files." Her character seemed to have abandoned all femininity in the show, however. Any romantic encounters that she ever had on the show were merely foils to Fox Muldar's escapades. She is, in essence, the straight man to Muldar's goofy persona. She was not a romantic character. Even when she became pregnant in the series, the child's conception was a mystery. (Presumably the child was the result of an alien abduction.) Muldar was definitely the more sexual character of the two, as he at least had an extensive porn collection.
A stereotype seems to be fostered that states that submissive women are "rewarded" with romance, and independent women "punished" with a lonely and unromantic life. This stereotype is prevalent through out all media.
The same can be said for other strong female characters, such as Mary Tyler Moore, Murphy Brown, Uhura, and Seven-of-Nine. The message appears to be that if you are an independent thinking woman, you are not attractive.
Batgirl From the old "Batman" TV show is an excellent case in point of this phenomenon. A cold and distant librarian by day, Barbara Gordon eschews the Dewy Decimal System by night and becomes the confident and defiant crime-fighting Batgirl. Batgirl is hot, Barbara Gordon is not, and neither seems sexually attainable. Batgirl is brassy and defiant, and Barbara is so intelligent that no man would ever find her attractive. Note also that Batgirl is another example of the "Miss Jones Syndrome," by way of Clark Kent. Take the glasses off of the librarian and put her in a clingy outfit and she is instantly desirable!
It's also worth noting that the Batman TV series was high camp and rather silly, and Batgirl's role was usually to get captured and the rescued by the final episode. She was only allowed to kick or push villains in a fight - she was not allowed to punch them. The writers thought it would make her look "unfeminine."
From the cartoon series "Scooby Doo," Daphne Blake (AKA "Danger-prone Daphne") is the coy and demure ghostbuster that is eternally captured and saved by Freddie, the male lead that is cryptically wearing an ascot. Velma Dace Dinkley is the resident genius of the group, and is often the member of the team that deciphers the clues and solve the crimes. She is also lacking in self-confidence, and is considered sort of clumsy and annoying by the rest of the team. She is a comedic foil to Daphne's damsel-in-distress. The smart girl is unattractive, the attractive girl is not smart.
Perpetuating the same stereotype, but in reverse, is the television program "Daria." Daria Morgendorffer and her younger sister, Quinn, embody the same stereotype that Daphne and Velma exhibit, except the lead of the show is the mousy girl in the glasses! Another show that has broken this same mold is "Ugly Betty."
"Buffy the Vampire Slayer" and "Xena Warrior Princess" differed from these other show's in that the female leads in these two shows bend the rules of the adventure genre, a female is controlling the narrative and fighting the battles usually reserved for men. In these two shows the female leads are portrayed as fierce warriors, more able to fight in battle than their male counterparts. The appeal of the show is the novelty of a female character portrayed as a dynamic and heroic figure. Note also that thes are female characters portraying typical male character attributes, these are not realistic women portrayed in a natural setting.
Another stereotype the television portrays is called the "Betty and Veronica" syndrome, where two girls are in love with one man, or two girls are compared based upon their differing attributes. Veronica is a vivacious rich girl with sex appeal, whereas Betty is more of a dependable, down-home sort of girl. The male then becomes the central figure of the trio, with the two females competing for his attentions. This plot device is used to create an eternal sexual tension between the male and female characters without resolution.
The TV show "Gilligan's Island" had a similar competitive duo, with Mary Ann as the Girl-Next-Door, and Ginger as the Hollywood sex kitten.
As a quick final note, I would like to point out that almost invariably female aliens from outer space are sexy, and male aliens are much more likely to be ugly, threatening and made out of theatrical latex.
This is a Zaius Nation Reprint.