First, I would say that a good photography should be well composed. I mean that everything that should be there, are there, at the right place ; this is often translated by the rule of thirds or the golden rules (rectangle, spirale, triangle,…) that is a kind of basic to make a good photography.
Then the photography should have some spirit, that is another basic, according to my definition, this is something that should be clever, something that make you think ; maybe another word should be intelligence.
Finally it needs a soul, that’s maybe the most important one (and different from the spirit), a photography that gives you the impression to be somehow alive, something that is talking to your guts and to your own soul, maybe it is like love, there are no words to really and properly describe it as it should be. For me the master for this is Todd Hido, he’s the one that move myself the most with its wonderful pictures (my favorite piece of work is Excerpts from Silver Meadows)
So to be a (very) good photography we need the three mentionned above, I’ve seen many photography that are good in composition but without any soul and any spirit. The other way around is true also, but I would say that a photography that has spirit and soul but no composition are not bad because they give me some emotions, make me ask myself something and to my opinion that are the most important.