Do all LCD monitors look bad when rotated 90 degrees?
Solution 1:
There are two issues.
First, the arrangement of subpixels - Microsoft's ClearType is optimized for horizontal arrangement of subpixels. I'm not aware of any LCD panels that are made with vertical subpixels. You might be able to configure ClearType to lessen this problem.
Second is the viewing angle of the display. There are different LCD technologies, and the cheapest don't have very good vertical viewing angles. When you rotate the display, those vertical viewing angles become horizontal viewing angles.
Solution 2:
Yes and no. Most consumer LCDs are based on the TN lcd panel technology (cause it's cheap) which doesn't have very good viewing angles. You can generally determine if you have a TN display by looking off center (up or down) at your lcd and if it appears that changing the viewing angle the brightness/contrast/color changes as well, then chances are, you have a TN. Now, when you rotate a TN, those vertical angles become horizontal angles and since your eyes look at the screen at slightly different horizontal angles, the monitor would look pretty bad. (I had a TN monitor mounted on a pivot arm and i basically had to look at the monitor at an angle to be able to read something in a portrait mode .. looking at the monitor straight on would give me a headache after a while since my right eye would see the monitor darker than my left eye. Looking at the monitor off center with the top of the monitor closer to you gives better viewing experience)
However, if you have an MVA panel lcd (or even better, an IPS based one), portrait mode would look so much better so in this case, the question to your answer would be no. Basically ... it's the old saying - you get what you paid for. If you are going to buy monitors that you want to use in portrait mode, make sure you buy one with excellent vertical viewing angles (i.e. get an IPS or MVA based lcd panel).
This site has brief description of the common lcd panel types if you are interested in reading more about it.
Solution 3:
There are three types of LCD panel: TN, VA, IPS
These are in order of increasing cost and (generally) increased quality of image, so TN is the worst quality but cheapest, and IPS is the best quality and most expensive.
TN monitors have pretty terrible viewing angles, and so rotating one 90 degrees will give the change in quality you mention -- viewing them from anything but fairly straight-on will mean that colours start to go very strange and possibly inverted, and brightness can vary a lot across them.
So, to answer the original question:
No, not all LCD monitors do this. Just the cheap ones!
edit: TN panels generally have poorer viewing angles in the specs, so they are likely to say something like "170 degrees vertical/160 degrees horizontal" rather than the 178/178 which VA and IPS panels will state.
Solution 4:
It might be due to the TN panel in the monitor which leads to bad angles, so when you tilt it you get it horizontally instead of vertically which might be more unusual for your eyes then the bleeding and color-distortion you get when looking at it the normal way. It's the same for me when doing it at my university's monitors and probably something you can't get away with when dealing with TN panels.