Exactly what it says on the tin
The Bourne Identity – Bourne vs the Professor
This film is here for similar reasons to its inclusion in my top 5 chases; it was a very smart sequence that was completely different from over-the-top action films of the time. Bourne only shoots four times, two of which aren’t even at his opponent… a thinking man’s gunfight.
Equilibrium – Final gun fight
I’m referring to the gun/martial arts mash-up with the main villain at the end. While ridiculously over the top, it was extremely slick and showed that a well choreographed fight could look just as good as a special effects extravaganza (see number four) for a fraction of the budget.
A Better Tomorrow – Restaurant shootout (I’ll link this one as it was hard to find a clip that hadn’t been blocked for copyright reasons – http://www.filmsmasharchives.com/musicvideo.php?vid=7d500b70c)
Another very smart scene (though with significantly more than 4 shots fired). This film is an excellent early example of the Heroic Bloodshed genre of Chinese cinema and this scene in particular is a perfect example of why John Woo rose to be one of the big names in that genre.
The Matrix – Lobby fight
Although many of the quirks in this fight (e.g. dropping guns rather than reloading them) were not particularly original (see number three on this list), this scene turned a lot of Heroic Bloodshed tropes up to eleven and introduced them to a western audience.
Reservoir Dogs – Stand Off
The shortest gunfight on the list… kudos to Quentin Tarentino for making this split second shootout awesome by ratchetting up the tension beforehand.