The usual rule of thumb for photographing wildlife is to get eye contact, and the eye should be tack sharp and have a catch light. Snap those photos when that animal is looking directly at you. It makes for a very powerful image and a wonderful experience in nature.
But I believe rules in photography are meant to be broken. So I also take photos of animals looking in different directions in addition to the direct eye contact.
Some of my favorite photos of wildlife are those that make it seem like the animal is pondering his/her existence in a vast landscape. I also like the portrait shot when the animal seems to be looking just beyond the camera - like a buck looking for a doe or a mountain goat kid looking for his mom.