I used to turn off my Plinius amp every two weeks when the cleaning ladies came just out of paranoia and immediately turn them back on after they left. When I talked to the Plinius service guy (yes there is one in the US even though their sales efforts have focused more or Asia/Australia/New Zealand) he told me not to turn it off ever - they don't go anywhere near the equipment, but I was worried just in case there was a new person in the crew.
They are very well designed and use minimal electricity when not playing. He said that powering everything up puts stress on the parts and will make the amp age faster. Of course he offered to recap and update everything in my amp (even though everything sounds better than ever). SS amps can last for decades without worry. That's the beauty of them - plus some sound really nice.
Other amps may not be as well designed - check with the manufacturer. Fans, tubes, whatever may have different recommendations. For me, I'd hate to have to wait an hour for warm up time. Often, I'll just play one record or a side. Turning everything on and off for that is nuts.