So, I have to admit, I sometimes have geeky tendencies [stop you snickering, really, stop]
Fire needs oxygen to burn, so if you're in the atmosphere less void of space [In space, no one can hear you scream, because sound needs atmosphere to propagate], can the gunpowder ignite and cause a gun to fire a bullet?
The explosion that fires a bullet does require oxygen for combustion, but it does not draw it solely from the air. Rather, some oxygen comes from an ingredient of the gunpowder itself, called saltpeter (potassium nitrate). The spark produced when the gun's hammer strikes the cartridge ignites the saltpeter and converts the oxygen in it to its gaseous state. This explosion generates a shock wave that propels the bullet out of the gun. [Note: lack of oxygen also makes explosions in space the rarity - looking more like a flash bulb as there is no atmosphere to transfer the energy to and cause the oxygen rich fireball.]
Care must be exercised though, because basic physics (Newton's Third Law) states that for every action there is an equal and opposite reaction. The kickback from firing a gun in space would send your entire body flying backward. Because there is nothing to slow the bullet in a zero-gravity vacuum, it would travel much faster and farther than it does on Earth, and so would you.
The visualization of a body hurtling backwards is what caught my minds eye while reading about this in the FYI section of the March issue of Popular Science. I just cannot get the image out of my mind of the shooter drifting out of sight :o)