#1
It's just something I was wondering... are guitars usually meant to be one or the other; does it matter at all? Is one better or worse than the other? What would it depend on?
#2
Guitars are mostly mono instruments. They have one output jack, so they can't be stereo. You can make it stereo in the mixing process, but I'd suggest two different takes of the same thing panned one left, one right, it will be more natural so. Just copying the same track and panning it the other way just makes it twice as loud mono.
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#3
The vast majority are mono. There are some tricks like sending each pickup to two amps, or using a stereo delay or chorus to make a mono signal into a stereo signal, but most of the time it's a mono signal all the way.

Stereo is a lot more common in reproductions of music than in the performance of music itself - most instruments either don't have the capability, or don't need, to be "in stereo." Acoustic instruments can't be in stereo*, so generally electric instruments follow that convention. It's often impractical to use a stereo setup for live electric performance, and the effect is significantly less impressive live than it tends to be with headphones or a home speaker setup.

Think about it this way - if you go to the orchestra, you experience that music in many dimensions. A stereo recording tries to replicate the effect by using two sound sources. Electric instruments are a bit different, but the idea is roughly similar: it is either impractical to move sound in such ways, or it doesn't work because there is much less precise control over the acoustics. Stereo works quite well when you have headphones on, or are using a home speaker system, where the listener is within a well-defined envelope where the stereo imaging can do its job. In a concert venue, you have thousands of listeners, and the acoustic properties of the hall are such that you could not possibly stage the sound such that they'd all get a nice, discrete left ear/right ear listening experience.


*I say that acoustic instruments "can't be in stereo" but that's a simplification. Strictly speaking, they produce sound from one source, but they are "more than stereo" when experienced live. You can reproduce an acoustic instrument in stereo, but what that does is merely reproduce the effect of distance and dimension that would have been lost with mono. With perfect stereo, you could reproduce those dimensions exactly, but you are not adding any information - just more perfectly reproducing it. What that means is that "adding" a stereo effect to a live instrument is a type of illusion, like a 3D movie. You experience actual life in 3D, so to reproduce it in a 3D movie can be more interesting, or might exaggerate aspects to make them look more impressive, but a stereo rig doesn't actually change the number of dimensions you experience.
#4
Thank you very much for the replies!

The curiosity arose, as henrihell probably deduced, with regards to the recording process. It makes perfect sense but not having thought about it before, I've had it happen that I recorded something using a mic and ended up with a Mono mix that sounded a bit odd.