Wasn't sure what was meant by this thread title, as the terminology "game camera" sounds like something quite different than the language photographers use to describe their gear. I think probably it would be more meaningful if the title were "Wildlife Photography" or "Deer, Elk, Moose and Other Game Animals" or "Shooting Wildlife," or "Shooting Deer, Elk, Moose and other Game Animals." Something along those lines, maybe?
I have very few photos of deer -- no moose or elk, though!
Here's a sweet little deer that I shot years ago when we were in Cade's Cove in the Great Smoky Mountains. Don't recall now what the lens was, but we were fairly close to her so I imagine it was my 70-200mm f/2.8 VR (Nikon) on either the D3 or the D300.
Again at Cade's Cove, very early in the morning before too many people had started coming in. This deer suddenly decided to cross the road and we were on the road off to one side, starting to shoot when a car came along over a hill, realized what was happening and promptly stopped to watch, too.