There are hundreds of threads on Audiogon that treat the issue of "on/off" versus "24/7 operation", some of which are considerably more thoughtful than this one. For sound quality, the vast majority of equipment sounds better when left on 24/7. Whether a component will last longer if turned on and off or left on 24/7 is more complicated and component-specific.
With respect to solid-state amps, a knowledgeable tech will explain that some parts used in amps benefit from on/off, and others are harmed by it, but that on balance, the parts that matter are better protected by leaving the component turned on 24/7. Generally speaking, output transistors on amps are harmed by on/off because they expand and contract as they heat up and cool down in response to being powered up and down, and they are the most complicated and expensive component to replace (they can be a challenge to match, and some have even been known to go out of production, leaving an amp without a required replacement part). Switches and relays tend to wear out more quickly if a component is powered up and down. Capacitors definitely wear out more quickly if an amp is left powered up, but they are relatively easy and cheap to replace.
Most digital equipment needs to be left powered up 24/7 to have any chance to sound decent on a high-rez system.
Regarding tube gear, it is a myth that tube life is always extended by turning equipment off - it depends upon whether you're talking about equipment that uses small-signal tubes like preamps and DAC's (many if not most are best left on 24/7) or tube amps (output tubes pass a relatively large amount of current and wear out fast if left on 24/7). The relevant question is how much voltage the tubes are run at in a given circuit compared to the tube's design maximum - if voltage is low relative to the tube's voltage limit, 24/7 can greatly extend tube life, as the voltage rush upon power up can beat the hell out of them, and the thermal cycles they experience as they are powered up and down are generally undesirable.
The Model 2/6/8/9 vintage of Rowland amps, like many amp designs, left the input stage powered up automatically if the amp was plugged in - this was described as "standby" - but the output transistors are powered down in standby and thus experience harmful thermal swings if the amp is used in this fashion. I left my Model 6's powered up 24/7 for three years except during electrical storms and vacations.
Running an amp 24/7 that idles at 200 watts will raise your electricity bill by $5 to $10/month, depending upon wear you live - it's like running a couple of 100 watt incandescent light bulbs 24/7. Of course, 24/7 operation is not green, and speaking of protecting equipment, if your gear is plugged in, whether it's turned on or not, it can be definitively roached by surges from line problems or electrical storms.
Again, there are very learned threads in the archives about this subject - you should look at them if you care about protecting your equipment and getting maximum performance.
