It depends on the piece of gear. I've had an amplifier [Odyssey Stratos] that would sound like ass for three days if it ever was powered down and allowed a chance to cool off significantly. The current amplifier I have sounds great as soon as you hit the power button, so I don't have to keep it on 24/7. As for shortening the life of the caps? I would imagine much of that has to do with the design/topology of any particular amplifier but I haven't seen or read any conclusive theories as to which one is worse [turning it on and off constantly -vs- just keeping it on 24/7].
When you get into tube amplifiers, or if you do, turn them off when you are done listening. Always unplug the entire system when a lightning storm is threatening and make sure the PC's are as far away from the actual outlet as possible. Lightening is so frequent down here in Charlotte that I always unplug the rig when I am away from the house. I have already lost a couple of amplifiers due to lightening, so I speak from experience on that one.
In search of accurate reproduction of music. Real sound is my reference and while perfection may not be attainable? If I chase it, I might just catch excellence.