Ranked by IQ

The use of IQ as a qualification or 'proof' of superiority. Thanks in part to the common belief that IQ is a flawless, accurate representation of every aspect of human intelligence and partly because it's an easy way to show an intelligent character's arrogance, a character might use his or her supposed IQ as an argument for their taking control of a matter, or otherwise being better than others.

The characters who do this will usually be on the border of Improbably High IQ, if not over it. If it's aliens doing this, it can be part of a Puny Earthlings routine.

In Real Life, by the way, IQ is a relative measure; the average is always 100. While we're at it, "genius" is kind of a vague term as an official assessment of intelligence; it's generally accepted that the line is at either 130 or 140, but there's no actual agreed-upon documentation making it official.

Anime & Manga

 * A variation of this happens in Baka and Test. Students are assigned to a corresponding classroom depending entirely on the score they received during the entrance exams. The smarter students get better amenities and classroom equipment.

Literature

 * In the book Ender's Shadow, the Battle School commander creates resentment toward young Bean from his classmates by revealing that Bean scored highest among them not just on IQ, but on every aptitude measure but one -- that of physical ability, since Bean is much younger and smaller.
 * Mack Reynolds' novel Brain World. The planet Einstein was settled by people who had a minimum IQ of 130, and they've been improving their average IQ ever since. When Einstein applies to join the United Planets, Section G sends Doctor Horsten and Ronny Bronston to investigate because the computers say they have the highest intelligence ratings of all of Section G's agents.

Live Action TV

 * Used in the Red Dwarf episode Holoship. Crew members of the holoship state their IQ along with their name and rank, and there seems to be a positive correlation between IQ and rank.
 * In The Big Bang Theory, Sheldon often uses his IQ as a 'proof' that he's correct.
 * In The Paper Chase, when James Hart first meets him, Franklin Ford III boasts of having an I.Q. of 190 as a sign of his superiority.

Tabletop Games

 * GURPS uses "IQ" as the short-form name of the Intelligence stat -- a measure of all forms of intelligence, independent of culture or species -- although it has barely any relation to actual measures of IQ. Apparently it wasn't meant to.

Video Games

 * In the Commander Keen games, Big Bad Mortimer McMire brags that his IQ is 315, one point higher than our hero (which is 314 in tribute to Pi).

Western Animation

 * On The Simpsons, Springfield is left under the control of local Mensa members after the mayor skips town. They disagree on how the town should be run and eventually start arguing by stating their IQ at each other. Frink insists his 199 IQ qualifies him to be in charge -- but is soon "outranked" when Stephen Hawking arrives on the scene!