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1) Lighting is key. If it's too dark, we can't make it out, no matter how good of a shot it was intended to be. Additionally, if it's too bright, it poses the same problem. I like my photos with an appropriate balance of lighting and shading.

2) Angle. It is what makes the photo. If the camera is tilted (i.e. not horizontal or vertical) the shot becomes ruined, as you catch too much of one thing and not enough of the other. Additionally, it should not be too close, unless its a close-up, or too far, unless its meant to capture the scenery.

3) Height. Never should a camera be placed on the ground. It just does not work. Additionally, if you're too high from what you intend to capture, it will also ruin the shot, as it'll look like you intended to capture the ground. The camera should be at face-height, even if you are taking a picture of yourself.

Those are mine.

To be completely honest it is all a matter of opinion, some people stick to different things to what they think makes the best photo, so depending on the situation anything is possible. Personally I think what is best about taking a photo is the thought that goes through it, sometimes you can plan all you want but it is that slight mis-take that will lead you to your best.

"To take photographs means to recognize - simultaneously and within a fraction of a second - both the fact itself and the rigorous organization of visually perceived forms that give it meaning. It is putting one's head, one's eye and one's heart on the same axis." -Henri Cartier-Bresson

Lighting is definitely the most important, hands down. Without light there is no photography, so it would only make sense that knowing how to identify, create and use good light is essential to creating a good photograph. An interesting subject and a concept that is inspiring to myself and others is also important to me in the photo. I want a subject that attracts the viewer and a concept that will provoke them to speculate a story.
I think to a degree it's important to have all of the technical skills down such as knowing how to control your shutter speed, aperture and ISO, and also knowing what role each take in creating the photo. When it comes to the "rules" of photography, such as the rule of thirds, or what is too much or too little retouching, or if a photo should even be retouched is very subjective. I however feel that good retouching is essential to creating my own art.

If it's a documentary style or actually any style of photography it should never be blurry, it lowers the standard of the photograph.