Are human eyes the best possible camera? I am not a physiologist, but whatever little I know about human eyes always makes me wonder by its details of optical subtleties. A question always comes to mind. Are human eyes the best possible optical instrument evolved by natural selection? Is there any possible room for further major improvement as per the laws of physics in principle? Can there be any camera prepared by human beings which can be superior to human eyes?
 A: This question can’t be answered exactly properly.  The eyes we humans have evolved to be “about” the best available to us hominids.  There are other species of life with eyes better adapted for their econiches.  Eagles and hawks have eyes capable of far better resolution at great distances.  They can soar 500 meters above the ground and spot a small animal for prey, where upon they dive from that height to snatch it.  Our eyes are nowhere near that sharp.  On the other hand their eyes may not be as adapted for fine resolution of very close vision.
Human eyes have some funny aspects to them which illustrate how evolution selects for adaptive feature built from previously existing structures.  For instance, the optical neuron innervates the eye from the front, which is quite the opposite of what one might expect.  It would be as if one built a CCD with the pixel connections connected in the optical path.
The best answer which can be given is no, but the eye is evolved to work within the limits of what is biologically adaptable.
A: The human eye is an indifferent camera. Compared to a hawk's, it is laughable. A hawk can sit on top of the Empire State Building and make out a dime on the sidewalk.
What makes the human eye any good at all is the software behind it: what our brains provide. You do realize that what really focuses on our retinas is an upside-down, tunnel-vision image that our brains sort into the images that we think we see, right? And that in experiments, people who were made to wear glasses that made everything look upside-down adapted in a few days so that upside-down looked right-side up?
We recognize patterns, colors, shapes where cameras only record differences in color and tone. It is not the eye that is remarkable. It is the brain.
A: This question is sort of difficult to answer in an objective way, because it depends very strongly on your definition of "best." Natural selection favors traits which provide a reproductive advantage; no more, no less.
Could our eyes be better by the standards of modern optical design, in terms of precision and features? Sure. I could easily design a camera with a larger aperture, better resolution, less abberation, a broader wavelength sensitivity, etc. There are even some precedents for this in nature. Some animals can see ultraviolet or infrared; some can even detect polarization (mostly birds I think?). I believe there are some fish that can swivel their eyes around through nearly a full circle in any direction. Cats and dogs have higher sensitivity in low light due to the reflective layer behind their retina, and squid have eyes with truly huge apertures.
It is worth pointing out though that the human eye, despite what I've said above, is still a pretty good camera. It can re-focus pretty quickly, it's got a fantastic image processing computer attached to it that can do incredible amounts of pattern recognition, noise reduction, and image stabilization. While its wavefront aberration is not perfect, it is pretty good for a biological system. They have very low chromatic aberration, and are quite compact. Additionally, our eyes have a curved focal plane (our retina) which is a lens designers dream -- it eliminates the problem of field curvature, which is an inherent aberration in any optical system that is nearly impossible to eliminate.
A: a few different answers:


*

*no, it's easy to imagine small improvements: more regular lenses, wider spectrum sensibility, more than three color sensors...

*not only not the best possible, but also have some fortuitous bad choices, the most commented is the retina orientation that makes it easy to detach with a big impact.  the very similar but independently evolved squid eye has the retina backwards, making it a lot more resistant.  unfortunately there seems no way for evolution to flip it without many blind generations in between. obviously not a good evolution path...

*best for what?  for producing images that will be seen by whom?  IOW: if the end observer is a pair of human eyes, then it will always be better to observe directly than to use an intermediary, no matter how high the quality/resolution/contrast/etc of such an intermediate reproduction.  (unless you want to see things not visible to the naked eye)
A: *

*This is a common misconception -- evolution has not stopped a million years ago leaving all the creatures in the "best possible state"; it is a continuous pursuit of adapting to the current environmental conditions, with only aim in reproductive success. Moreover most of the population stays in even more suboptimal surroundings due to random mutations (the advantage of that is to achieve faster adaptation).

*Yes; even a huge one, see Georg's answer. Squids have eyes without blind spot and with no risk of retina detach. Bees see light polarization and some UV. Cat's eye has a mirror that doubles the signal strength. Etc, etc.

*Human eye has about 2Mpixel resolution -- my phone's camera is better.  Of course this is not a fair comparison, since the most usability of a sight stays in the brain, but if we talk about the eye itself...
A: [Updated to correct a couple of mistakes pointed out in comments. Thanks!]
At my age, it's clear that there's room for at least one major improvement: more accommodation. Accommodation, in this context, means the ability of the eye to focus at different distances. This is accomplished by changing the shape, and hence the focal length, of the lens. The lens material gets stiffer over time, so that most people lose the ability to focus on nearby objects as they age. In addition, of course, many people, including me, lack the ability to focus on faraway objects.
If I were in charge of natural selection, I'd make those muscles strong enough to let me focus on nearby objects. Presumably, back in the savannah, the decreasing ability of middle-aged people (or, as they were known back then, very old people!) to focus at objects less than a meter away had little effect on the number of descendants those people produced.
Another natural figure of merit to use to assess any optical system is how close it is to the diffraction limit -- that is, how close it comes to attaining the best possible resolution for a system of its size. I'm not an expert, it looks like the eye is within a factor of a few of the diffraction limit (example), so there's a bit of room for improvement there, but not much.
Another thing to look at is the quantum efficiency, effectively the fraction of all incident photons that an optical system uses. Again, things depend a lot on conditions, but in general the eye's very good on this score, reaching levels of about 10%. (That may not sound so great, but I think it's hard to imagine ways of improving it dramatically.) 
Another way to improve the eye would be to boost the range of frequencies it could see. Going into the ultraviolet probably wouldn't do much good, but if you added some infrared receptors on your retina, your night vision would be much better.
