I have read stuff that posited that hunters have front eyes (I think the reason given was for more accurate depth perception), and that prey-animals have eyes towards the side of their head to give a wider field of vision.
I'll see if I can refind any of that stuff.
I didn't find exactly what I was thinking of (I think it was probably a book), but a section of the Binocular vision wikipedia article has some information (uncited, unfortunately). Specifically:
Some animals, usually but not always prey animals, have their two eyes positioned on opposite sides of their heads to give the widest possible field of view. Examples include rabbits, buffaloes, and antelopes. In such animals, the eyes often move independently to increase the field of view. Even without moving their eyes, some birds have a 360-degree field of view.
Other animals, usually but not always predatory animals, have their two eyes positioned on the front of their heads, thereby allowing for binocular vision and reducing their field of view in favor of stereopsis. Examples include humans, eagles, wolves, and snakes.
Some predator animals, particularly large ones such as sperm whales and killer whales, have their two eyes positioned on opposite sides of their heads. Other animals that are not necessarily predators, such as fruit bats and a number of primates also have forward facing eyes. These are usually animals that need fine depth discrimination/perception; for instance, binocular vision improves the ability to pick a chosen fruit or to find and grasp a particular branch.
I was wondering whether the rules might be different for sea creatures because of hydrodynamics. Practically all fish have their eyes on the sides of their heads. It's possible that understanding hammerhead sharks and flounders would be too hard.
Puffer fish are fish which have eyes at or near the front of their heads, but they aren't built for chasing things down. I just found out that you can get a puffer fish to chase a laser. I don't know what that proves. Maybe they chase relatively small slow prey.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.