Would you be responsible for damage to your friend's professional sound equipment while you were transporting it to a job for him?

This depends on what state you reside and also what state the incident occured in. IF you carried the property as a friend and not as a hired mover AND the damage was committed by no fault of your own, in most states this is considered to be an accident. The friend may not win a lawsuit against you in this case.

IF you were paid or hired to move the equipment in any way then you are most likely at fault and will be held responsible.

Depends on the situation. If the transportation was done at the request of your friend, and the "service" was done for the sole benefit of your friend, then you could be considered an agent for your friend. If so, then his insurance should cover at least part of the cost of his damaged equipment.

Also a point to note, is how the equipment came to be damaged. If you dropped it while loading it into a vehicle is completely different from if someone crashed into the back of your equipment-loaded vehicle at a stoplight, causing the damage.

I would think that if you're a transporter/mover professionally and/or own/work for a company that provides such services, would be pertinant. If you were paid a fee over costs, would factor in as well.

If you were simply doing a friend a favor, for free, and were involved in an accident with another vehicle, the negligent parties insurance carrier would cover damages to property (if you were at fault, your ins. carrier should pay-friend would need to receipts etc. proving cost and age of equipment). If that's not the case, surely your friend has his "professional" equipment insured and they would pay.