As you get further from a square, you get less screen area for a given diagonal. A 4:3 screen with a 19" diagonal gives you 173 square inches, but a 16:9 screen with the same diagonal is only 156 square inches. http://daleswanson.org/things/screensize.htm So it's all about picking the biggest possible number for the crummiest product.

They used to be. Mostly machines with dedicated monitors. Nice, beautiful square screens with gorgeous square pixels.

http://www.old-computers.com/museum/computer.asp?c=298

I have 2 24" monitors and almost always maximize everything to full screen or snap windows side-by-side (Win-Left / Win-Right).

You don't need a large screen if you're going to leave all that space unused.

Because you have two eyes

Because televisions aren't square.

More precisely, because eyes (plural, operating as a single input) aren't square.

16x[9/10] sort-of matches the field of view we have.

Subjective, I know, but 4:3 was a lot more pleasant to work with, at least for me. 16:(9|10) might match movie aspect ratios better and thus would be better for watching them, but I do other things more often than watching movies on my computer screens (it's different for a TV, though).

Conversely, 16x(9|10) allows me to put 2x portrait documents next to one another comfortably. Alternatively, I can work on a document with a 2-page view.