Pentax K-3

Very true... K-5 shots can easily be cropped square if
you want square shots

APS-C lenses would almost certainly vignette with this setup. Don't forget that the area covered by a lens is generally circular, the 'image circle'. A square or rectangular sensor has to fit within the circle. If you simply make it square based on the longest side of the ASP-C sensor, you're going to end up with a diagonal that's greater than the diameter of the circle. You'll therefore have vignetted or worse 'chopped' corners.

If you can't visualise it then draw a circle and draw a rectangle inside it, such that the corners of the rectangle just touch the circumference of the circle. Then draw a square whose sides are the same length as the longest side of the rectangle. You'll see that the corners are of course protruding outside of the circle.

It might work with some lenses but I seriously doubt it would work with the likes of standard kit lenses, lenses like the 55-300 or anything in the ultra-wide focal range (ultra-wides being already configured to get the greatest possible angle of view within the limits of the image circle available).

Edit: Sorry didn't notice Pentaxophile already covered this ground. Don't mean to step on anyone's toes!

Once and for all I'm NOT saying that I particulally want square photos. Also as to the lenses then the old 35mm film lenses would possibly do the job OR, Pentax could make new lenses as they have done for APS-C size. All I'm saying is that if (ALL CAMERAS) were square format as many of the old medium format ones were then anyone could take photos with the camera in the same position and not have to turn it to potrait or landscape which would be much easier on a tripod or monopod and then they could crop to whatever shape and size they wanted. I know you can do that now but wouldn't it be easier if all cameras took square photos.
I'm sorry I started this now as so many of you got the wrong idea of what I was getting at. CHEERS Vic.

On reflection, I see that vignetting/non vignetting is not so clear cut. If DA lenses just have enough coverage for the current APS_C sensor, then yes vignetting will occur. However there is a massive difference in the circle which covers APS-C and the circle which covers full frame. The DA lenses that work on full frame with only minor vignetting will would very easily give full coverage of a square sensor with a side length equal to that longest side on APS-C