Lockheed AC-130 gunship is a heavily armed ground-attack aircraft variant of the C-130 Hercules transporter. The plane is manufactured by Lockheed and converted by Boeing. Why are most of the guns in AC-130 installed on the left-hand side (but not right)?
It is not designed to strafe, it is designed to loiter over a target or, to apply suppression fire or support fire for a sustained period of time.
It often circles a target area and a counter clockwise orbit (circling to the left) makes sense since the captain sits on the left and can keep the area in view at all times.
Therefore, the weapons are mounted on the left.
Traditionally, the doors most used on an aircraft (including civilian ones) are on the left (captain's) side. Often weapons are mounted in door apertures so that additional holes do not have to be introduced into the fuselage. It follows that there are more, more accessible, pre-existing holes on that side of the fuselage.
The AC-130 is the evolution of modified C-47s from the Vietnam War. At the time, a small group of USAF personnel explored arming cargo aircraft with side mounted weapons in order to bring greater firepower to bear for ground support. In particular, they wanted to solve the problem of strafing, where aircraft can only bring their firepower to bear for a short period of time, and often without a great deal of time to aim.
Captain Ron Terry was in charge of the initial effort which adapted these planes to gunship use in Vietnam in 1964:
Terry arrived at Bien Hoa Air Base near Saigon on December l. After the miniguns arrived the following week, he selected two test crews of six flight members and an interpreter, and two C-47s with relatively low flight time from the 1st Air Commando Squadron. The planes were modified to accept three minigun pods along the port side (two in the last two windows and one in the cargo door); an MK 20 Mod 4 gunsight mounted in the left cockpit window; and a selective trigger placed on the pilot’s control to fire one or all the guns.
Since AC-130s are now specially converted from C-130s by Boeing, and they use modern targeting sensors (IR and visual cameras), and that windows/doors are no longer large enough for the custom mounts they use to install the weapons, there's probably no specific reason for keeping them on the left except that it's the status quo.
All the guns are on the left side. The method of targeting is that the aircraft circles counterclockwise so that the left side is pointing downward. Thus all the guns can be brought to bear on the target (unlike an old frigate with guns on both sides) and the pilot can see the target as he circles.