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. You may photograph your lover, but for us to be interested in the photograph, there has to be something that we can see that is interesting - we can't see their personality - the interest has to come from the composition, the pose, their appearance. the print has to be interesting minus the feel of the wind, the warmth of the sun, the smell of the pines.
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) a good photograph tends to have a sense of rightness to it - 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. So 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 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- I'm uncomfortable even writing that since I am a great believer in the highest quality printing standards, but there's some truth that the better the image, the less dependent it is on pristine quality. Yes, perhaps pepper # 30 benefited from being shot on 8X10 instead of 35 mm. with a fast film, but I'd bet it would still look great. I have never seen pepper # 30. Oh, I've seen many's the reproductions and certainly the better ones show you more of why it's a great photograph - but none look bad. 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?'
10) And last and most importantly - 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, but greatness is also a matter of luck. There's a certain something in a truly great image which comes not from the photographer being clever. Sometimes photographers create magic.
Are you ready to create magic?
I will say again, all of the above 'rules' are open to deliberately breaking one or all of them (though it might be tough to create a great image that breaks every one), but for the most part, this is the way to bet.