I read a few years back that cab drivers in London grow a larger hippocampus in their brains as they gain what's known as "The Knowledge" (of the city's roadways), but I hadn't heard of any similar thing going on with musicians.
According to neurologist Oliver Sacks, author of Musicophilia: Tales of Music and the Brain, musicians' brains differ from those of the general population in a number of ways, including having a stronger connection between the left and right sides of the brain (from an NPR interview):
"Gottfried Schlaug - up at Harvard... used brain imagery to measure the sizes of different parts of the brain. He found first, for example, that the corpus callosum - the big band which unites the two hemispheres of the brain - tends to be larger in musicians. And then he found enlargements of the cortex, the grey matter, in the auditory parts of the brain, and in motor parts of the brain to a degree which may be almost visible to the naked eye. So that, say, if one looks at pictures of brains, you might not be able to say this man is a genius or this man is a fool, or this man is a visual artist, but you could probably say that man is a musician."