I voted when it's done for Food. However, most people I know who do it do it for sport...and food (or pelt).
My brother-in-law use to shoot Coyotes when he lived out in Utah, apparently they're pests out there, and he kept every pelt from the animals he killed. I was amazed at how warm them keep you. So, while I kind of think that hunting nowadays is kind of silly (unless you live in a rural area) I have been impressed with the quality of the meat/fur from the animals people have hunted.
I'd probably do it if I could bow hunt, hunting with a rifle and scope, and hide, and salt licks, and beer just seems like cheating to me.