Does anyone leave their amp and preamp on all the time?

Tube Research Labs builder and founder also told me it was easier on the tubes to stay on.  The way he used the 6sn7 tube in the preamp sure gave it long life and I did leave it on.  

Many amps and preamps have warm up cycles of a minute or less so that the tubes are brought up to full power slowly. How would this feature figure into the leave on/turn off debate?

It would figure strongly! My TRL preamp did not have this feature and the on/off cycling was indeed robbing the tube of more life than just leaving it on. Like all things audio....it always depends and few things are just black and white.

Wow...didn't expect this would be a debate, but it's a good debate. 

I used to worry about it, but these days, I really don't. Back when I had my quicksilvers, I just made an educated guess that turning them on and off more than twice a day was about the same as leaving them on, as far as tube wear goes. I could be wrong, could be right. 

Off and on IS hard on tubes...but, so is playing them. At idle...not so much.

Obviously, designs vary on how hard the tubes are driven, right? 

I pay my electric bill, I pay my taxes, and I pay for my stereo stuff. Sometimes I gotta leave it playing to break it in. Like doing laundry.

My big 125 watt tube amps have a 45 second warm up.  Once on, they take about 20 minutes to reach maximum set bias.  Although they run cool enough to put your hand on the transformers (Class A/B), the tubes only last 2500 hours.  So, I do not want to run them full time or pay for the excess power used (I do have solar covering most of the year except the summer when a 9000KV system just isn't enough in inland SoCal).  I leave on my Bryston BIT20 isolation transformer all the time as it uses nominal power when no load is asking for power.  I used to leave my EAR 324 phono stage (solid state) on all the time as well but have switched to a tube phono stage.