"Don't even think about it!" is a phrase commonly used when a person denies another person something. Usually the phrase is used as a proactive response to a question before it is asked, as in, "I know what you're going to ask me, and it's not worth your time, because I'm going to say no."
In 1993, Shaquille O' Neal, a popular basketball player, made a Pepsi commercial in which the phrase was prominently used. The commercial begins with Shaq at a street court playing hoops, and a little kid notices him. Then the kid exclaims Shaq's name, and Shaq, noticing the kid has a Pepsi on his hand, walks over and says "Hey, can I have it?" He bends over, supposing that his admirer will give him the soda, but then the kid, out of nowhere, says Don't even think about it! Then, a musical sound simulating that of a scratched record erupts, ending the commercial with the Pepsi logo and slogan.
This commercial was rather popular, and it was shown on TV for about three more years.
The commercial is actually a parody of another famous commercial from the 1970s produced by Pepsi's rival, Coca-Cola, in which a young boy meets football player Mean Joe Greene as he is leaving the field after a game. The boy gives his hero a bottle of Coke and, in exchange for the drink, the football player throws his towel to the boy, who excitedly catches the souvenir.
The phrase also appears in series 4, episode 5 of Men Behaving Badly, when a drunken Gary climbs into bed intent on having sex with the sleeping Dorothy, who it is revealed is wearing a T-shirt with the phrase written on it in large letters.
Visitors to New York City are known to have been amused to see a road sign with the text "Don't even THINK of parking here". This is an actual road sign which means that people are prohibited from parking next to it. It has been used in other North American cities.