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What is the benefit of this?
Assuming you mean rotating monitors ;):

On a widescreen monitor, say, 1680x1050, rotating it 90 degrees yields a 1050x1680 screen, which is very useful for viewing longer documents, for seeing more code, etc. If what you want to see is taller than it is wide, a portrait-mode display is very useful.
 
Or are you referring to monitor speakers? I know some people put them on their sides instead of upright, but I don't know what the pros / cons of this are.
 
I mean monitor speakers. This is the digital audio section.
 
quite simply, monitors should be placed on their sides if they sound better that way. that's more room and position dependent than design dependent, but check with the manufacturer to see what they recommend.

if your next question is, "should the tweeters be on the inside or the outside?", then, again, it depends on what sounds better (though i do believe tweeter-outside is more common). just make sure the monitors are placed to be mirror reflections of each other.
 
It is a good idea to try and get the tweeters to be in an equilateral triangle at the same height as your head. Turning your speakers on their sides can compensate for height or width restictions in your set-up and help you get closer to the golden triangle.

If you do do this, you shouldd of course check that it does actually improve the sound, but with most near-field monitors you should definitely notice an improvement.
 
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