There used to be monitors made mainly for desktop publishing (remember that?) that swiveled to vertical orientation or horizontal, as desired, along with video drivers that adjusted to suit. I haven't seen even a photo of one in years. Seems like a good idea for some things, like editing vertically formatted images.
They are still being made: http://www.amazon.com/HP-W2207-22-inch-Widescreen-Monitor/dp/B000OK6T9W