I turn my gear off when not in use, and I have never had a tube go bad even after 15 years of regular use. Of course, I cannot say that I would have had a shorter life for my tubes if I left them on all of the time; I have no comparative data. There are many ways for a tube to fail, but eventually all tubes will exhibit lower emission of electrons from the cathode due to aging; turning off gear when not in use reduces this kind of tube degradation. If an amp is designed correctly, the early failure from the effects of being turned off and on (e.g., thermal shock) should be reduced enough that it makes more sense to turn off the amp when not in use. As for other components, heat can degrade some components and this will favor turning equipment off to reduce exposure to heat, but, some capacitors might fair better without being turned off if they are susceptible to damage from high inrush current.
The vast majority of tube gear manufacturers will recommend turning off gear when not in use. The downside mentioned by those who don't recommend turning off their gear is usually not so much shortening tube life as it is performance is affected until the gear warms up. The gear I am familiar with usually sounds decent after five minutes or so of use, but, I am aware of some gear that takes much longer than that to warm up (supposedly an issue with the capacitors taking some time to fully reform and stabilize).