These days, some displays allow you to rotate them between landscape and portrait orientiation.
At work, I have a 24 inch TFT in portait mode which I use mostly for coding (and other tasks where vertical space is valuable). It is very nice, because e.g. in text processing, a whole page fits the screen nicely.
In a way, we have that with tablets and phones, too.
Operating systems and drivers will allow rotation of most monitors and it mainly comes down to a matter of mounting hardware if autorotation isn't a big deal. Monoprice has a stand for about $20.
There is an non-obvious caveat to using vertical monitors on Windows though - ClearType font rendering doesn't support vertical subpixel arrangements, so you're stuck with naive anti-aliasing.
Color subpixel font hinting is on its way out. Windows 8 and 10 stopped using it for UWP (including the start menu / start screen); DirectWrite doesn't use it (font rendering in Edge and Firefox); Office 2013 doesn't use it.
Certainly screen rotation (with windows tablets and phones) would involve a lot of inefficient re-rendering. But i think the official reason was that since the subpixel colouring effect depends on the background colour, it's hard to animate transitions efficiently.
On a high-DPI screen, you'd be hard-pressed to notice the difference compared to greyscale hinting. Colour subpixels were a great hack, but high-DPI is the proper solution to this issue.
I've got 3 Dell 24" monitors that can be used in portrait mode. (U2412M - 95dpi 1920x1200 eIPS - not expensive. But many Dell monitors come with this sort of stand.) When I had a desktop PC with 2 GPUs I had them lined up that way in a row. It have to say it was a bit menacing at first - it's about a 48" diagonal. But, you know... you make do. I took a few pictures at the time but the only one I've got handy is it running Doom: http://ffe3.com/pics/.3monitors/IMG_1327.JPG
In the end I missed the horizontal space often enough that I've now settled on having at least one full-size - i.e., not laptop display - landscape display in the setup. (Currently I've got my laptop, 1 x landscape in front of me, and 1 x portrait to the side.)
If you're going to do this, I guess you want to buy IPS-type monitors to minimize colour discrepancies due to the wide range of viewing angles you'll be using. eIPS is supposed to have a 170° viewing angle, but the colours on mine still aren't quite consistent from side to side (or top to bottom as it is once rotated). If you've got a TN-type display I imagine it will be even worse.
Also might be worth buying all your monitors at once. I bought mine over a couple of years; the colour temperature is very slightly different on each one, even when using the factory-calibrated settings, and one has a noticeably different anti-glare coating.
For years I've used an old 19" LCD in portrait mode next to a new-ish 24". The display heights (after rotating the 19") are identical, and the vertical resolutions are almost identical (1080 vs 1024). It's a cheap/free way of getting a wider screen. Usually I keep some paper or reference document on the 19" and have two side-by-side terminals on the 24".
I worked on screen saver engines that had to support these - We did a lot of direct access to the bit mapped display for speed, at the cost of compatability. That being said, there were OS hooks that made responding to the rotation easier.
The problem came in when running applications that didn't respond correctly to the configuration changes - since we had patched the os (transparently, particularly when not actually driving the display) we got blamed for a lot of application crashes and ended up debugging and sending very explicit bug reports to other software vendors.
When the iPhone came out, I was deathly afraid of the screen rotation for about 6 months, convinced as I was that 50% of the apps wouldn't respond gracefully. (And I personally have never found one that failed here.)
At some point (I believe Windows 7), Windows started allowing the use of ctrl-alt-arrowkey to rotate the display. I think it depends a bit on the graphics drivers, but I also think most "standard" drivers (ie: Intel, Nvidia, AMD) supports it out of the box. It can be a bit confusing if you hit ctrl-alt-downarrow (invert screen) by surprise... (ctrl-alt-uparrow is the shortcut for standard mode).
That happened to me when I was 11 using Windows XP. Since I couldn't figure out what I did I resorted to turning my monitor on its head for about a week.
