I was going to just pop this in as a comment, but what the heck, I think I'll battle a little against the idea of objective metrics. Objective metrics are good things for camera reviews, not so much for photographs because you take the art out of the equation with this concept. People have listed some good, relevant, factors in what makes a "good" image, by definition, and yet you could follow every single measure and still produce an image that is utterly lifeless and dull.

In this century we're often obsessed with hard numbers, quantifiable information. Cameras, today, can operate at speeds and in conditions that cameras in the golden age of film could not and so far beyond the ability of early cameras that you almost can't compare. There are images from these bygone eras that would fail some of these objective tests, such as sharpness, noise, grain, etc. and still they're masterpieces of the photographic art. Sometimes, imperfection is what makes the image something special! Lomography is premised on this very thing and there have been some seriously stunning images taken with toy cameras that will fail all of your objective tests. There's also Lensbaby, creating lenses to do the opposite of what many would cite as objective criteria for a good image.

So, in my opinion, there's really only one objective measurement for the quality of an image in my eyes: does it evoke something for me. That's all. It can evoke wonder, intrigue, the science geek in me, the romantic, whatever, but when an image makes me take a longer look at it, then it's a quality image in my book. I can be objective here, the only emotion that causes me to ignore is "blah" and I know it when I hit it. :)