A couple of examples of the "gangsta grip". Click on images to enlarge.
In the above two images, we see two people demonstrating the infamous sideways gangsta grip style. Some people think that this style of holding a handgun originated in the 1990s, but it has actually been seen in movies made in the 1960s as well. For example:
Marlon Brando as "Rio" in the movie One-Eyed Jacks released in 1961
Eli Wallach as "Tuco", the ugly guy in the 1966 classic cowboy movie, The Good, The Bad and the Ugly, starring Clint Eastwood
While these movies did briefly show characters using the sideways grip, it was the Hughes brothers 1993 movie "Menace II Society", that really popularized it. It was after Menace II Society was released to theaters that it started to appear in a lot of other Hollywood movies, TV shows and rap music videos.
Russell Crowe demonstrating the sideways grip, from the movie No Way Back.
One theory on why this shows up a lot on film and videos is because it allows the director to show a dramatic view of the actor's face as well as the firearm, all in the same scene, as can be seen in the picture of the movie poster above. If the actor was holding the pistol vertically, a larger portion of his face would be blocked by his hand and the firearm. Another theory is that movie actors and stuntmen don't wear protective eye-wear during shooting scenes and many got tired of getting hit in the face by a hot cartridge and so they started shooting sideways, so that the empty cartridges would drop to the ground.
So why is this grip such a bad idea. Well, if a user holds his handgun like this, then he cannot use the sights of the weapon. There is a very good reason that firearms have sights and they are there to help the user aim the firearm properly. Accuracy suffers a lot, as demonstrated by the Mythbusters TV show here:
As you can see, it may look cool in the movies, but in real life, the sideways gangsta grip is pretty darn useless unless the user is very close to the target.