As mentioned, the Golden Mean is probably a format that easily "acceptable" to the human mind. Sort of a primal thing. But perhaps for more impact another format would draw attention because of it's "discomfort" level.
Personally I crop everything, shot mostly Hasselblad square but never printed square, and still shoot for a little "coverage" of what I'm seeing on a full frame digital sensor. Used to print 16x20 but now more 16x24.
I couldn't think of anything witty to say so I left this blank.
Interesting question really. I've realized for some time that I tend to prefer more squarish and less rectangular ratios than most people. I find wide screen TVs and computer monitors too wide - whether this is something in the way I see or just my aversion to change and the fact I'm used to the more traditional rectangle I don't know.
I do like 4x5"ish" proportions and sometimes, but less often, the 35mm ratio. Anything wider than that strikes me (usually) as contrived and too "stretched." You can try to get the impact of a big outdoor scene for example with a wide panoramic ratio, but it seems to me you're just cutting off the sky and/or ground to do it, and that's often not worth the trade. Really wide screen movies look to me like I'm viewing the action through a slit window.
Since getting my TLR I've found I often enjoy the square format. I happily print square or crop in any ratio that suits me. I'm not averse in the slightest to cropping. Scenes don't come in pre-packaged ratios. If a crop lets me eliminate a distracting element or otherwise make a more pleasing composition, I'll crop away.
The comments about circles are interesting. I've seen (recently I think - a link here?) some circular images I thought were incredibly good. It would be hard to visualize that at the time of shooting with my 35mm, but an overlay for the TLR might be possible and very easy for the 4x5. I have thought of making a 4" circular mask for the ground glass, and shoot some negatives intending to print that way. But how would I get a circular easel?? I guess I look for a smooth, evenly cut circular mask of some kind, which may not be easy to find or make.