The following has been paraphrased from an article written by George Barr, a professional photographer whose website can be found at www.georgebarr.com.
Below are some characteristics common to many (but not all) good photographs. There are definitely great images which break one or even all of the rules, but you'd be well advised to consider these rules and ignore them only when you have a specific reason to do so.
1) The photographs are interesting
I don't mean the subject matter. There needs to be something in the print to catch your eye. The interest has to come from the composition, the pose, the appearance, the colour.
2) Compositions are simple
Any item in the picture has to reinforce the main theme, not stand on it's own as another interesting detail.
3) There tends to be a sense of rightness
The various parts are arranged in a pattern which makes sense. It may not be harmony or balance since that's not necessarily what you aim for, but there has to be an organizing pattern to the arrangement.
4) It's uncommon for a great photograph to have harsh lighting
Unless you specifically want harsh lighting, you'd be well advised to avoid it. This doesn't necessarily mean you can't photograph at noon, you just need to plan.
5) Great colour photographs usually have a limited palette of colours which work together
When colours are similar, they have to be very similar, when not similar they need to be complementary - more or less opposite on the colour wheel.
6) Great photographs show the unusual or the unnoticed
Either the subject is something most of us don't get to see (because of travel or not getting up early enough) or it's so ordinary that we tend to pay little attention until someone points out that the old warehouse has interesting shapes, patterns, shadows, etc.
7) The best photographs don't need big cameras and fine printing
The better the image, the less dependent it is on pristine quality. I think we sometimes hide behind careful technique, using it as a substitute for making great images. I know for myself, when I was younger, I tried to solve my problems with going to 4X5 instead of learning to see better.
8) Great photographs often have a message
It may only be - see how pretty this flower is - in which case the image better have shown the flower to advantage, revealing it's beauty. The message may be one of passing on a feeling - of tranquility or anger, disgust or excitement, joy or sadness.
9) A lot of really good images make you wonder
Where is he going? What's round that corner? What is she thinking? How did this happen? What is it exactly that I am looking at?
10) the truly great photographs are mostly taken by people who take a lot of good photographs and who are ready for the rare great image
Greatness can be a matter of luck - sometimes there's a certain something in a truly great image which comes not from the photographer being clever, but from the photographer being lucky. But, as a famous golfer once said - the more I practice, the luckier I get ...