Depends on the situation. When I'm elk hunting, I shoot until they're down, unless I know for a fact that I hit them hard in both lungs or the heart. I've heard many a tale about elk being hit in just one lung, the liver, ect and they weren't able to recover the animal until several days later when the ravens found it or they weren't able to recover it at all. Elk have a lot more meat than deer too, so its not quite as big a deal to put more than one bullet in them IMO. A family friend once told me that on elk, the best thing you can do is crowd the shoulder on your shot- if you hit just behind, you get the vitals, if you hit the shoulder the elk might not die right away but it won't be able to go anywhere and you can put another round in the boiler room to finish the job.

When I'm hunting deer and antelope, however, I only shoot once. They dont' stand up to my 7mm Rem Mag nearly as well as elk. The only time I'd ever consider making a follow up shot is if I knew I hit it too far back or I was on the edge of the reservation. I've never had either problem, though, so for me one shot is all that's necessary.