Megatokyo, AD 2032. Seven years after the devastating Second Kanto Earthquake, the rebuilt city of Tokyo stands as a symbol of the wealth and power of the commercial behemoth that dominates it, the Supernational GENOM Corporation .

Genom's best known products are the "Boomers", biomechanical humanoid constructs combining the power of a mechanized form with some of the intellectual faculties of a human being. Initially developed by the brilliant Dr. Stingray to aid humans in the exploration of space, the Boomers have since been redefined for warfaring roles by GENOM (with an eye to lucretive arms trading).

Disastrous incidents involving rogue boomers have plauged Megatokyo for some time, finally leading to the formation of the Armored Defense Police (AD Police) as a response. Though well equipped with an arsenal of Helicopter gunships, a massive arsenal of high-tech weaponry and armored vehicles, the ADPolice have nonetheless had only limited success in dealing with Boomer rampages.

In contrast, a less official (and often more effective) counter to the Boomer threat is offered by a shadowy group known as the Knight Sabers. Sometimes operating as mercenaries, more often as vigilantes, these high-tech commandos use powered armor Hardsuits to battle renegade Boomers and similar threats.

-taken from Adam Warren's BGC: Grand Mal and changed slightly

The Bubblegum Crisis was the first chapter in this Blade Runner themed anime. Practically the entire concept was taken from the brilliant movie by Ridley Scott, which is based in a almost anime envisionment of the future where humanity has come to greatly rely on artificial humanoid constructs called "Replicants", which were also initially created for space exploration, their uses became apparent for all sorts of menial tasks from then on as soldiers among other more... intimate roles. A ship flown by by a group of Replicants returns to earth after killing the human crew and hijacking it. Their objective? Unknown. A specialized officer (played by Harrison Ford) is called in to deal with them, he is what is known as a BLADE RUNNER. A highly recommended movie that offers a much more insight into that which is the Bubblegum Crisis.
How can you tell that the BGC is based off of Blade Runner? Well if the basic plot wasn't a dead giveaway, there's the fact that one of the more popular Replicants in the movie was a female named Pris (in BGC the series is focused on Priss. Coincidence? I think not). Also, if you've watched BGC you'll notice that Priss' band (at least in the original series) is called "Priss and the Replicants". But despite what that might make you think of the series, the BGC was FAR from a rip off as the series stands firmly on its own and set the standard for quality animation in Japan with a top notch story and voice acting. BGC opened up a whole new world while borrowing a few key points from Blade Runner, such as the dark, shadowy and altogether depressing place that was Los Angeles in the future. Which has more than a few places that partially resemble the Genom tower and other buldings in Megatokyo. But again, that's scenery. The plot circles mainly around a group of armored vigilante women who wage a private war against a corrupt corporation. There's also tons of side trips with sentient boomers, evil scientists, triad asassination attempts and more to keep them occupied in the entirety of this eight episode OAV series.
Why only 8? A big lawsuit broke out following the 8th OAV making it impossible for any work to continue on the series. Much later came the series BUBBLEGUM CRASH which was intended to sort of... give closure to the BGC series. While the 3 part "Crash" didn't exactly succeed, other more successful series have spawned from the BGC. They are as follows: AD Police Files (3 pt OAV), Bubblegum Crisis Tokyo 2040 (TV Series) and the recent AD Police (TV Series).