heritagecameras
Newbie
I've always shot transparency film, and I have always longed for a 6x6 projector. For projection of images, the square is vastly superior, filling the screen fully and identically from one shot to the next. (Square format 126 Instamatic film was also good in this sense.)
Another option that was popular many years ago was the "Superslide". These were 40x40mm images taken on 127 transparency film, fitted into a standard 2x2" slide mount suitable for many quality 35mm projectors. At over 1.8x the area of a 35mm image, these made the best possible use of the available area covered by these projectors, and filled the screen very impressively. I remember being wowed by some of these superslides at the local camera club's competition night about 50 years ago, taken (if my memory isn't playing tricks on me) with a 4x4cm Baby Rolleiflex TLR.
Here's a more recent experiment with the format: They Still Shoot Super Slides, Don't They?