How far can a bullet fired from a gun travel before gravity and air friction bring it to the ground?

If you point the gun straight down it'll hit the ground very soon. It all depends on what angle the bullet was shot out at and the velocity of the bullet comming out of the barrell.

there are far too many missing variables here for an answer. just a few of them would be..

what gun?
what bullet?
what type of round and the grain weight?
what angle it is fired at?

It depends on how high the gun is above the ground, and how high the terrain is downrange. But keep in mind that gravity acts independently of horizontal motion, so if you fire a bullet horizontally from say 10 meters high out across a level, flat field, and drop another bullet from that height at exactly the same time, they both will hit the ground at the same time.

If the ground slopes up or down, or the gun is aimed up away from the ground, or towards it, all bets are off.

If you're pointing it at the ground and shoot, then not very far. :) It just depends on the trajectory, wind resistance, and gravity. Wind resistance can be more or less depending on the direction the wind is blowing.
Also, got to account for bug, bird, animal, building, person resistances as well.

assuming you shoot it perfectly horizontally
d= 1/2 a*t^2 where d = height above the ground, and a = 9.81 m/s - solve for t.

The drag is negligible, and your bullet will take the same amount of time to "drop" to the ground as if you dropped a ball. So, how "far" basically depends on how far your gun can shoot.

If you're trying to shoot it up, then it becomes trickier. You'd have to estimate the vertical component upwards.

You'd want to solve using
using d= Vot+ 1/2a*t^2. and Vf^2=Vo^2+2*a*d where Vf = 0, and Vo = the initial vertical velocity from exiting the bullet. Unfortunately, this equation neglects air friction/drag/resistance.

To do that would be trickier. You'd need to know what the the velocity of a bullet as a result of drag could be. From wikipedia, you get something really ugly.

http://en.wikipedia.org/wiki/Drag_(physics)

But, you can probably neglect this, unless your bullet is really large, or you're shooting over a very large distance.

For a bullet

If you mean holding the gun parallel to the ground and firing, the bullet would hit the ground at the same time as one dropped from the same point of origin.

I have heard and read that the range of a bullet is one mile, ever see that on a bullet box ? I have never actually tried shooting a gun to find out.

it depends on the force that the bullet is fired with .
if the force acting on it was high the bullet will go for along range.