leave power on?

What Jax2 said X 4!

Tubes: turn them off
Solid state: leave it on

SIMPLE

With tube equipment it simply has to do with the cost of retubing. Better to turn off tube equipment and warm it up for a short while prior to listening, unless you will be doing a lot of listening during the course of two or three days, such as weekends, where the thermal issues associated with turning off and on are probably harder on the tubes than leaving the unit on for such a period. This last recommendation comes from one of the people at ARC who provides information over the phone.

This subject has been hashed out several times.

The bottom line seems to be:
Turning it off and on all the time is as bad as the heat damage from leaving it on 24/7.
A tossup.

Leave tube gear on 24/7 if you have a large bank account and little worry about the cost of re-tubing with the good stuff. Otherwise, turn it off. After an hour of warm up, I doubt in a blind test you'd be able to tell the difference from a unit left on 24/7.

If you have solid state gear, then it likely sounds best if left on 24/7, but the "green" question comes into play. How much natural resources are are you comfortable wasting during the many hours you're not listening?

It's a personal decision.

Lots of folks driving Hummers. Lots of folks driving Prius.