I would always turn off amps that are not going to be used for a long time. First, for safety reasons, the amps should not be left completely unattended for long periods. Second, heat will, to some extent, shorten the life of the other non-tube components, such as capacitors and resistors. Third, he cathode of the tube, which emits the electrons, have a limited capacity to do so which is wasted at idle; most preamp tubes are not run really hard so they have a pretty long life, but, given the cost of decent tubes, it makes sense to not waste them; also, some designs actually run preamp/linestage tubes pretty hard, so that tube life may actually be as short as one-year, so conservation really makes sense there. Finally, it makes little sense wasting electricity as heat from running gear unnecessarily (tube gear is works inefficiently as space heaters).
The reason that one might have for leaving gear on is that it does sound better when fully warmed up and stablized at full operating temperature. The good news for tube fans is the gear actually warms up pretty fast, compared to solid state stuff, so that most gear sounds very good within 10 minutes or so of turn-on. If your listening habits involve frequent short-term interruptions, that might be a reason not to turn the gear off and on at every interruption.
I know there are those who are concerned about shortened tube life from the "surge" at turn. The analogy is to how light bulbs rarely fail in the middle of use; they almost always fail at the instant of turn on. With tubes, this is somewhat different. Bulbs are designed to come on instantly--when the filament is cold, it conducts so easily that the surge at turn-on causes abrupt temperature changes that causes the old, weakened filament to fail. This is, to some extent true for tubes as well, but, they actually light more slowly and do not suffer as much from thermal shock.
To the extent there still is some concern with turn-on stress to tubes, different equipment design has an impact on this as well. Gear that uses tube rectification in the power supply inherently turn on more gently. The rectifier ramps up the current/voltage to the rest of the gear instead of creating an instant-on situation. Some gear may also include circuit elements designed to ramp things up slowly, such as thermistors in the power feed that slowly increase current flow as they heat up, or circuits that don't allow the plate voltage to be at full strength until the cathod/heater are fully heated (if the plate tries to pull electrons from the cathode before the cathode is heated and readily delivering electrons, damage can occur to the cathode ("cathode stripping"). These turn-on issues are usually bigger issues with power amps than with preamp/linestages.
