Leave it on?

There is no issue with tube amps--they should be turned off when not in use because all tube filaments have a limited life and tube amps warm up fairly quickly.  With solid state, the answer is a bit more complicated because life of transistors are not as significantly shortened by being in a quiet on condition as compared to tubes, and solid state gear does take longer to warm p and sound its best.  But considering power consumption and safety, one may still prefer turning it off when not in use.  Another thing to consider is electrical storms or other times when power is acting up--if you are not home to shut off gear, you will be exposing it to dangerous conditions that may damage electronics that remains on and even the speakers from resulting excessively loud pops. 

The only thing I leave on all the time is my streamer because that is what the manufacturer recommends (they say it take a very long time for capacitors to fully charge and reform if the gear is shut off).  The rest of my gear is tube based and there is no question that it is better to shut off completely.

Invalid,

Your personal experience represents a small sample size.  Also, it sounds like you experience a lot of tube death in order to detect a pattern.  Is it possible that your gear is hard on tubes, particularly at turn on?  If your gear has tube rectification, turn on of the rest of your tubes will be inherently gentle.  Some tube gear have “soft start” circuits that slowly ramp up the juice.  
Almost all of my gear uses tube rectification.  I’ve been running the same amp and linestage and phonostage for 15 years and I have not replaced any tubes.  I cannot draw any conclusions from personal experience with that kind of data.

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).

There would be a problem if the preamp/linestage emits a thump when it is turned on or off and your amplifier is on and sends that thump to your speaker.  If it is loud enough, it may be annoying, or even worse, damaging.