The popular phrase for a cross eyed person round here is “One Looking at you, the other looking for you”. But why cant we move our eyes independently of each other? I know its not the most practical thing to be able to do, and would causes severe diziness and inertia, but is there anything physically stopping us? Most people can move their eyes inwards, to look at their nose (the classic Duh face) bt why cant we have one eye looking over each shoulder? It seems to me that its something psycologigal rather than physical stopping us… I can, for example, raise my right eyebrow in a Roger-Moore stylee, but not my left. Are the muscles on the right of my face stronger than the left, or is it just a case of habit, that when the left eybrow raises, both raise? Eh?
Who says we can’t move them independently? I can do it, just no reason to do so - my brain can’t seem to process two images, takes a bit of concentration but with practice you should be able to as well.
Have fun.
Because our visual system is “wired” for binocular vision. You might be able to train yourself to move each eye independently (although I’m somewhat dubious), but as you suggest it would serve no useful purpose. Given how dependant primates are on depth perception, it would be a disadvantage to have to independantly control both eyes to maintain depth perception and focus on an object. Going “cross-eyed” is just an extreme case of focusing on a very near point.
By the way, I’m not sure where “inertia” enters into the problem. Perhaps you meant a different word?
No, seriously, it’s not that hard to move just one eye at a time - Just takes practice and a big sister to gross out (aka “incentive”). Moving them both, chameleon-like? Physically, why not? Practically? Ouch! I get a headache moving just one eye.
Eye movement seems to be easiest to control by tracking an object, so the hard part is trying to focus on two things at once. Do that and then slowly move one or both of them and your eyes will be moving independently.
I haven’t mastered looking over each shoulder, as my eyes are on the front of my head - YMMV. 
I can move one eye at a time. I cross them, and then I can move one back and forth while the other stays crossed. I can’t move them both at the same time, and I can’t really see anything when I do it. It’s also kind of uncomfortable.
I 'spect he meant “vertigo.”
When I was about 15, I met a girl about my age who could move her eyes independently, like a chameleon. She did say it gave her a headache, but she could do it. It was unsettling to see.
I don’t know if she had “taught” herself to do it, or had always had the ability.
Some of us just have the gift.
As asked previously: why would you want to? The human brain isn’t very good at linking up more than one image. Your vision works nicely when your eyes are properly lined up for binocular vision (eg, two very close-but-different perspectives with the same focal point): you get nice depth perception and perephiral vision and whatnot.
I think (just based on my experience with a whole big buffet of eye problems while growing up) that if your eyes aren’t all lined up that way, your brain is pretty much going to ignore half the input its getting. This immediately means that your perephiral vision and depth perception are reduced. If it’s a prolonged state then the eye that the brain is “ignoring” may or may not have reduced visual acuity, which is permanant: once your eye stops being so good at seeing that way, it’s really hard to fix.
I’ll stop now and let someone who has an actual education (rather than experience as a pissed-off and blind-as-a-bat 6-year-old) on the topic talk.
New (to me) info - see “interesting abstract” about halfway down this page.
Summary:
Predators generally have forward-facing eyes with binocular vision where both eyes focus on the same point, using parallax to help pinpoint the position. We fall into that same category, though can override the natural tendendcy with effort.
Prey animals usually have eyes set back farther on the sides of the head to provide wider-angle coverage to watch for hungy predators. I am not as sure as how independently their eyes can move but I would think so since there is no coordination between them. There seems to be little to no overlap in the field of vision of my guinea pigs.
I can move my eyes independently with some concentration although I can’t move them to be wider than parallel (don’t know anybody who can, besides the Marty Feldman photo posted above, although that was due to a medical condition).
I can do it. Can’t see worth a shit, and it hurts, but I can do it.