Generally speaking, no. But, copper is a fairly soft metal, so it
work hardens easily. What that means is if it gets stressed a lot (read: bent back and forth repeatedly), it hardens, gets brittle and breaks. Of course, that's
NFG, so in applications where the wire is going to be worked hard, you usually use stranded wire as it has much smaller cross-sections. By bundling a bunch of smaller strands together, you end up with a thicker wire or cable that can stand being bent around quite a bit and still have some
ampacity. It doesn't eliminate the problem, it just reduces its frequency.
In applications where the wire isn't going to be stressed, it doesn't matter. A good example would be building wire, such as in your house. That wire is put in place and never gets moved, so 99.9% of the time it's solid. Usually, inside a guitar the wire should never get stressed, either. But, some people like to take their instruments apart repeatedly to experiment with different wiring schemes, pickups, pots, etc. In that case, a solid wire could conceivably get hardened and break, so you might want to use the stranded variety.