Depending on my task, I may rotate the 1920x1200 screen in front of me 90° to 1200x1920. I find that much more useful for reading large amounts of text and/or code. The underlying OS supports it, the monitor arm this display is mounted on supports it, yet everyone on the job was remarking simultaneously how odd it was and how useful it seemed as they were shoulder-surfing while I picked through a large code-base. A full-screen Terminal window on this monitor in landscape mode is 270x81, which is just plain silly, but 81x270 in portrait mode is very, very useful.
I have two such rotated displays on my work desk side-by-side to get a 21" x 23.5 combined screen. The problem I get is that viewing angle on average displays is pretty week in the vertical angle (great, so nudge it up or down an angle) - but if you put it in portrait mode, this acute viewing angle really hurts - just moving your chair from one part of the desk to another can expose it.
Unless you're going with IPS displays, the portrait mode of a monitor is somewhat compromised.
I used a TN display in vertical position for a while and it sucked. If you moved the head just a little sideways the colors completely changed, and after a couple of hours I started to feel nausea. My doctor told me it was because the eyes are seeing different images (each eye saw the display at different angles, and because of the poor vertical view angles the brain received different colors and light and had to compensate - like using polarized 3D glasses). Now I use a combination of vertical + horizontal 16:10 IPS displays and it's way better. I mostly use the vertical one for web browsing and doc reading.
>A full-screen Terminal window on this monitor in landscape mode is 270x81, which is just plain silly, but 81x270 in portrait mode is very, very useful.
Except you are not going to get 81x270 characters in portrait mode unless the characters are square, as in Chinese script.
Very useful indeed. I use a similar 1680 x 1050 rotated 90º (so it's 1050 x 1680) with a browser. When I'm doing frontend work and having a browser fullscreen gives plenty of room for the viewport and web inspector or firebug. It's a real productivity improver.