From my days in college music classes, I was told that horn players (usually trumpet players) can develop a kind of callus around the lip area, due to pressure against the lips (cutting off the circulation) and the tightness of the embouchure. In extreme cases, this can form a lesion. I had a really tough time learning the basics of the trumpet because of the pressure. That and the breathing was totally different than in singing, and I couldn't get used to the breath control.

As for other instruments, I've heard of guitarists getting punctures on fingertips. I've also seen one or two piano players get repetitive stress injury, forcing them to wear a wrist brace, but the affliction's not as outwardly apparent unless you're wearing the brace.