Last month the movie Equilibrium showed off a nifty art they called
the Gun-kata.  Just curious if this was perhaps based on some existing
martial art.  It consists of weilding two pistols and
shooting/disabling lots of people, among other things.  Are there any
martial arts that practice the use of firearms?

The answer to this question is highly dependant on your definition of
the term "martial arts". As far as I know the asian martial arts are
very traditional, most follow what was invented a long time ago,
possibly long before the firearms were even invented. For example the
founder of kiokushinkai-karate served in the Japanese armed forces in
WWII, where he for sure had weapons training. When he created his own
karate school he went with traditional approach - no firearms. After
all some sources claim that the whole point of martial arts is giving
advantage to an unarmed person (this obviously does not apply to
bushido and ninjutsu). If you consider army special forces and police
training as a kind of "applied martial art" then here's your answer:
Most modern armies, police and anti-terrorist forces have training
programs for personnel who are supposed to engage their opponents in
close-range combat. Such training progams usually combine pistol
training with tactical trainig and a few other kinds of training.
Basically, you are not only taught to shoot well, you are also taught
how to move, look out and do your job while making it more difficult
to shoot at you. Speaking of weapons training in particular, the
students in such schools train to achieve intuitive aiming: you shoot
a gun by simply pointing it in the right direction, without of going
through all the trouble of aiming it. Once you've mastered intuitive
aiming, you start training shooting "with both hands" or as the
Russians call it "po-makedonski". This involves being able to
intuitively aim two pistols. Students also get trained in rapid
firing: they have to hit a target that suddenly appears for a brief
period of time and then quickly disappears. There is not a whole lot
of people who can do this, it's not anybody's fault, it's that
everybody's nervous system is slightly different. The percentage of
students that graduate is usually low.
Here are a few skills that one has to master to graduate (this list is
far from complete):
- Marksmanship: intuitive aiming, i.a. - both hands 
- Reflexes / Reactions, abitity to react quickly and CORRECTLY
- Tactical thinking: moving without of exposing youself, choosing the
right position, changing positions, etc.

A shooting frenzy using a pistol in each hand (preferably performed
whilst diving in slow motion) is a great movie cliche, but is just
that: a creation of the movies. Pulling it off in real life would be
near impossible, as it's too inaccurate.

Other than that the previous comment is very good.

Kurt Wimmer (the director) 'made up' Gun-Kata for the film.  He saw
that after Asian films had concieved that if an actor has two hands,
he could hold two guns, the whole pistol/actor interaction evolution
had just stopped.  He created Gun-Kata as the next step, the first
fusion between martial arts, firearms and the actor.  Given when Eq
was released, it's surprising that Wimmer was the first director to
fully merge martial arts and firearms into one discipline on film.