Your problem here could have a few very simple solutions. First, your projectile must be either a dynamic object, or a rigid body object. Static objects can not have angular or linear velocity.
Another solution could be that your projectile is getting lodged in the collision bounds of what is probably (in your case) a static character. The best way to make a gun turret is to have a static base that controls the rotation, a no collision barrel parented to the base, and an empty on the end parented to the barrel. Of course, you could just have your no collision barrel Emmit the projectile.
Logic setup of base
Logic setup of Barrel. Note- half of the logic here is simply to limit the rotation so you can not rotate the Barrel into the base.
Expanded view of the logic for Barrel
Logic setup for the Empty, Note- the property sensor and the property actuator are to limit the ammo, and do not really matter for this answer. Nevertheless, it is way more realistic and funner to have limited ammo, so Your ammo is limited.
Physics options for the projectile.
Notice that the X and Z location is locked. that means that the only way the bullet can move (only effects angular and linear velocity) is along the local Y. locking those two axes can be useful if you want to shoot lasers that do not drop due to gravity.If you want to have a hits based projectile instead of a physics based projectile, you can check the box enabling Ghost option, (below the actor check box) this will still register the collision, but it will not make the target physically react on collision. you could also then add a armor property to your target, and have each collision remove one of the armor points, then when the target's armor property reached 0 it could disappear. Locking the rotation along the X,Y and Z will only make the projectiles look more realistic if it is physically colliding with the targets.
If you had trouble following that, or simply want to examine the blend to see first hand how Everything works, you can always http://x.27 download the Blend file