As Frank says, lots of great pictures happen by chance--serendipity, if you will. However, good photographers know that you often have to create your own serendipity. Pros, for example, can't rely on chance luck to get the great shots they get. Being in the right place at the right time counts for most truly great photographs. I've taken literally thousands of travel photographs and know that getting a good photo often takes planning and knowing how to make the best of given situations. For example, I have prize-winning photo I took in the rain at night on Red Square in Moscow. No one else was out taking photos ("It's raining!"). The situation was serendipitous to me but, in most folks minds, not good for photography. I knew what to make of it.
As for equipment, yes, as Frank also says, it does not take expensive equipment to take good photos. There are lots of travelers taking nothing but snapshots with costly DSLRs. I've taken my share of "GWSH" (George Washington Slept Here) photos with my SLRs and DSLR. Yet there are times when good equipment is necessary for a great photo. Once on safari in Tanzania a woman kept urging the driver to get closer to the wildlife so she could get a picture with her P&S camera. I, with my SLR and telephoto lenses, was able to get photos she could not get without violating the animals' space.
I've had my share of lucky shots. And among them are some of my favorites. However, to get consistently good photos I cannot rely on getting a few lucky shots out of a thousand. I take photos with purpose and intention. Then I celebrate the serendipity when it happens. As someone who teaches a "Photography and Seeing" course, I know it's not the camera gods that make for memorable photos. Nor, is it the equipment, although that can enhance the chances of getting good photos. It's one's "eye" by which I mean one's heart and mind. Congratulations on your fortunate accident. I celebrate it with you. And yes, I also shoot with a digital P$S,