There are a million Audiogon threads that discuss the issue of whether to leave gear on 24/7 or to turn it on and off, and you should research them. Generally speaking, turning equipment on and off is in fact bad because it exposes it to thermal cycles, i.e., heating up when you turn it on and cooling down when you turn it off, which damages components over time. There are exceptions to the rule, however, for example, if you owned a class-A biased amp (Krell made many of them), it's best to turn them on and off because they run extremely hot, which is generally bad for components, and they burn too much electricity and heat up listening rooms to leave on 24/7. The only maintenance and longevity issue with leaving normal solid-state gear on 24/7 is that it reduces capacitor life, but caps are relatively easy and cheap to replace, and you can still expect to get many years of life out of them. This is greatly preferable to the failures that will result from turning components on and off, such as output transistor failure, which is expensive and complicated to deal with.
Many manufacturers will not advise users to leave gear on 24/7 because of liability issues, but many take the risk and do not even include on/off buttons on their gear - if it's plugged in, it's on. Other manufacturers offer a standby feature, but it's often done for marketing (i.e., to appeal to people that do not know any better), for example, putting many Audio Research CD players into standby does nothing more than turn off the display and mute the outputs - all internal circuitry remains powered up, as it should be.
Of course, it wastes electricity to run gear 24/7, but that's a different issue. And all equipment must be unplugged - not just turned off, but completely unplugged from the wall - in the event of electrical storms and when you leave your home for longer periods such as vacations.