I'm new to the hobby and I thought this would be an interesting discussion question. Greatness is subjective, of course, so I'm not talking greatness in terms of being ranked against all photos taken in the world (unless that's personally the benchmark you choose to rate yourself on). What I'm really asking is how often do you personally feel fulfilled with your photography? Whether you go out daily on photography walks, take your camera everywhere all the time, or just do a ton of professional gigs, what I want to know is how often do you think "Wow, I got a great shot there. I'm really proud of this one."? Do you have several every time do take photographs, maybe one a day, or is it few and far between for you? How do you feel about coming home from a photo session and feeling that you didn't really get anything good? For those that do professional client work, how do you feel if you finish a pro gig and don't feel like you got anything all that special (even though it may be good enough to warrant your professional standards)? On a second note, if you do professional gigs like weddings and such, do you ever aim to get something unique and original or are you more focused on making sure you get everything on your standard checklist of photos your clients expect to have?
To get a truly great shot that stands the test of time, it needs to be significant, captured with some degree of accuracy, and also a bonus if its lighting and composition are decent... Some have more weight than others, depending on what the subject is. (Tieninen Square, Mohamed Ali over Sonny Liston, Afghan Girl, and Half Dome to think of four examples.)
For most of us, that day may never come. However, I don't have any of those above four pictures hanging in my home. I have my family, that I shot with a remote trigger from my phone to my camera on a tripod at a local park. I have a large canvas of a beautiful tree that stands alone in a field not far from the house, in a snowstorm at Winter solstice. I have a rolling shot of my friends Ferrari 156 Sharknose that I took on a winding country road, from the back of a 2006 Chevy Cobalt, with the boot propped open with a snow shovel, that made it into Road & Track magazine.
Images might not be considered great to the masses, but they are great to us, and that's good enough for me. I look for the significance in the lives of both myself and those around me, and try my best to make them look as beautiful as possible. Shots people pay me for and proudly hang in their own homes, or use to represent themselves and their businesses, or to just be there simply because they are enjoyable to look at everyday. So I guess I do alright. Find the great in what's around you, but if you want to take great shots, it always helps to stand somewhere interesting with a full battery and an empty card.
Ha, after your first paragraph I was so getting ready to disagree with you. But after reading your entire post, I couldn’t have put it better myself!