I think the best general rule for a quick kill and anchoring game is to aim for the far shoulder with the lungs in between me and the shoulder. Try to avoid face on and face away shots. As 45MAN says, it depends on the gun. I like to use a big one!
Woods hunting sometimes presents a shot quickly and you cannot over think it. If the shot is close I usually aim about 1/3 to 1/2 way up. On a longer shot I usually go 1/2 to slightly higher. The older I get I find myself liking higher shoulder / spine shots. It usually puts them down DRT.
Being the hypocrite that I am I have successfully taken both face on and Texas heart shots although I do not recommend them unless you have enough gun to get full penetration. These shots can be messy and shooting too low can make for a long and possibly unsuccessful track. I have also killed quite a few meat does with well placed head shots but there is risk. You must have a solid rest and be able to hit the golf ball like wvhitman. As I said I do not recommend it.
"Therefore go and make disciples of all nations,... "
Handgun hunter since 1979 - haven't used a rifle since!
HHI member #992, NRA, SCI.