Should I leave my equipment on ?

All the comments above are great!
I just want to add a thought to the comments:
I have personally been wondering if part of the reason the amp can seem to take the longest may actually be the speakers crossover capacitors needing time to settle in? Since the amp MUST be on to actually have the speakers crossovers powered, it would be quite difficult to find out if it really is the amplifier, or the speakers themselves which benifit the most from the long "best sound" warm-up.

My amp has the power switch on the back encouraging me to leave it on.

Elizabeth, you're close! Actually, it's the coupling or storage capacitors in the amp/preamp, that take time to charge, stabilize, and reach optimum performance. The cross-over networks in most speakers are passive, and are good to go, immediately. Of course, new speakers will take time to "burn in" the cross-overs and drivers to reach optimum sound. And if you don't play your speakers for several days, it mat take a few hours for them, as well as your cables and interconnects, to reach peak performance again.

Thanks to all for such comprehensive answers. FYI what prompeted this question was, among other things, comments I've read from some audiophiles who stated their equipment has NEVER been turned off.

Here is a similar query- I'm currently evaluating different pieces of equipment and interconnects, etc. I have to turn some things off to switch things around. If the equipment is turned off for but a few minutes after it's been on for , say several days, is that the equivalent of a full blown cool down ??

Thanks again to anyone with advice for me.

Even if the equipment is turned off for a few minutes it usually means that it will require another 24 hours to stabilise on turning back on.