Popularised by film director John Woo, this method gained popularity during the latter half of the 1990s. The firearm's co-ordinates are transformed -90o in the vertical plane (for right handed hoodlums).

This breaks with traditional gun manipulation and offers the gangsta a new twist on a clichéd and tired format. Waving your gun in this manner is also far more sinister, your gun acting as an extension of your fist, your trigger finger unashamedly exposed.

Where this technique really kicks in is with dual action left and right handed usage. The extra stability afforded by the new position grants territorial crack dealers previously unknown ambidextrous abilities. The recoil from the weapon is absorbed by the whole arm, dramatically cutting down on friendly fire from overzealous automatic machineguns.

It is customary to document your killing spree on enormously high speed film cameras and view your subsequent carnage slowed down by a factor of at least two.

Although I have not seen any evidence, it can only be a matter of time before 180o degree transformations make their debut, although this does require the assailant to be double jointed to some extent.

Avoid highly subjective writeups. Firing a pistol in this style is a really bad idea, because it's more likely that the bullet casing will get caught in the breech instead of ejecting cleanly. If the casing gets caught, your next shot will probably make the firearm explode.

Initially, this method of firing a pistol or machine gun had absolutely nothing to do with accuracy, gunfight tactics, concerns over jamming, or the biomechanics of absorbing recoil. The business of holding a gun sideways was thought up while John Woo was shooting his action movies. Why? It was first done to keep actors and stuntmen from getting spent brass flung into their faces. Later, people kept doing it because they thought it looked cool.

If you've seen a John Woo movie, you know the actors fire off a whole lot of blanks, and those little metal casings get burning hot. On one set, Woo discovered that the particular gun models they had purchased for the movie were spitting spent shells upward. So, to minimize the chance he'd have to suspend filming indefinitely and take Chow Yun-Fat to the emergency room with a scorched eyeball, Woo just told him and the other actors to tilt the guns sideways so the brass ejected away from them.

Chow Yun-Fat looked like sex on a stick in those movies, so others (gangstas, American filmmakers, game designers) started copying him because he was so damn cool. Pretty soon, everybody was holding guns sideways purely to look like badasses, without any regard to whether or not it served any useful purpose.

In short, there's no sensible reason to hold a gun sideways unless you're shooting a movie on a budget and your props manager happens to bring you poorly-designed firearms.

Reference: John Woo's commentary track on his DVDs "Hard Boiled" and "A Better Tomorrow".