Green issues aside, from a purely technical point of view, professional equipment in recording studios, broadcast enviroments, etc, is never turned off. In fact the real pro stuff does not have an on/off switch and are even UPS powered in case of mains failure.
Damage can easily be caused by current surges when powering up and it's common knowledge that it takes a good while for high end equipment to become completely stable.
I'm sure you've all heard stories of someone's basement lightbulb lasting several years because it's always left on, as the filament inside is not damaged by the repeated expansion and contraction caused by the warming and cooling. When powering up, even home equipment cases a temporary surge in current, well excessive to what is normally used, which does eventually break down the chemical properties of internal capacitors and resistors, all of which contribute to an early electronic death of said unit.
As for the pollution/enviroment thing, I don't have the figures, but I'm sure it would cost a lot less and pollute less to keep an amplifier powered all year than it would to jump in the car and go for a drive for a few hours. But as someone pointed out correctly, when going on holiday or such, all electrical equipment should not just be turned off, but disconnected from the wall socket for safety reasons.