I seem to remember at some point seeing a military salute as being the hand pressed flat against the forehead, rather than the traditional perpendicular to the forehead salute. What countries employ this salute, if any, and why?
The proper salute in the U.S. Marines is not perpendicular to the forehead, but slightly canted downward, so that the person receiving the salute would not see your palm. Your upper arm is parallel to the ground.
I think you are thinking of a “British salute”, which I’ve never seen outside of movies and television.
It looks like this: Right hand, palm outward, back of hand to the forehead, fingertips either on the brim of a hat or on the far edge of the eyebrows.
Sound about right? AFAIK, this is still in use, especially among all of the former British colonial states. . .
Tripler
Can any British Dopers confirm?
The British Army and Royal Air Force salute palm outwards; the US forces use the same salute as the Royal Navy.
The Canadian military used to follow the British saluting style, and certainly were still doing so as late as the Korean War, but adopted the US style salute about 1967.
The Australian military (except the Navy, which uses a US-style salute), uses a salute as follows:
“At the position of attention raise the right arm in a circular motion at right angles to the body, bringing the right hand to the head, wrist straight, palm to the front, fingers and thumb fully extended and close together. The elbow is in one and square with the right shoulder and the forefinger and second finger are to be in line with and 25mm from the right eye”
Then: “Bright the right hand smartly down to the position of attention by the shortest possible way”.
One thing the DI manual does not make clear is the manner in which the arm is brought to the salute. The right arm is brought up, straight, at right angles to the body, so it is pointing to the right of the person saluting (make sense?). Then it is bent at the elbow to effect the salute. If there’s someone standing to the right of you, they will get whacked by your arm if they’re standing too close.
Taken from the Australian Air Force Cadets drill instruction manual.
I have never heard of any Australian military unit using a salute that requires the back of the hand to touch the forehead. For that matter I’ve never heard of British military people doing this either. It sounds like something you see on movies, and of course, you should believe everything you see in movies!! 
Max.
PS the AAFC drill manual can be viewed here.
Max.