I believe we've had this discussion before. My first camera was a Yashica TLR that took sqyuare photos on 127 film. I shot mostly slides, I have no idea where they are now, but I do have a lack and white print from then.
I later started shooting 35mm (I really wanted to be a photojournalist). Then about 8 years ago, I started working on a book and came to the conclusion that I wanted all the photographs to have the same orientation. So instead of shooting all verticals or horizontals, I cropped all the images square even though they were shot 2:3 ratio. I became addicted. Soon after I acquired an MF SLR and came back to film and I haven't abandoned the square format since. Except for street photography, almost all my work ends up square, no matter the original. I did make an excursion into the panoramic format (thank you Josef Koudelka). At one point, I worked on a book that didn't end up getting published, called Square Solace.
Here is the essay I wrote for the introduction:
There is an inherent equilibrium to the square format. No dimension dominates, it is balanced and solid. That alone brings a certain solace, a settled quality to the composition. What the photographer does within the square can maintain that peace or disrupt it by how he or she frames the scene.
At the same time, what I discovered when I started shooting square format photos is that the square is not what we expect to see, it is not our natural perspective. So it takes both the photographer and the viewer a bit off-kilter. The edges of the frame are more intrusive as it were--they are equally close, and composition becomes more obvious and important.
The traditional horizontal format feels natural somehow, maybe because we have two eyes positioned horizontally. But even the vertical format is familiar through books, magazines, and today’s smartphones. (I can’t get over the number of vertical videos that are shot, even though many are viewed on a horizontal computer or TV screen.)
Apparently constraining, the square format is actually a liberation. When shooting square, classical rules can be ignored, left by the wayside. A flat horizon running through the exact middle of the frame, a horizon that is wildly tilted, elements dead center, all these may become more valid in a square. And these new relations can challenge what we had learned to believe was there when we looked at the world.