Most tube gear sounds pretty decent within 10-15 minutes of being turned on so there is no good reason to leave the gear on all of the time--waste of energy and waste of the limited life of tubes. While there is a possible safety issue with leaving tube gear on unattended, the chances of a fire is extremely low, and such risk would apply to solid state gear as well.
Tubes are NOT like light bulbs, which come on instantaneously, so they are NOT as prone to thermal shock from being turned on. The tube may be subject to some damage from "cathode stripping" if the high voltage rail instantly powers up and the cathode is not yet heated enough to be emitting electrons. Better designs utilize a soft start circuit to prevent such problems, or if the amp uses a tube rectifier, the amp will naturally ramp up gradually. Overall, with most tube gear, there is more wear on the tubes from being left on when not in use than from the stress of being turned off and on more frequently.
What I never do is turn off an amp or preamp and then turn it back on without a fairly long interval in between (at least 10 minutes). I have seen tubes, particularly the rectifier, flash when this is done. While I have not noticed any permanent damage, this cannot be a good thing.