What is better for the computer - leaving it non-stop on, or switching it off every day after use?

If economy is in your best interest turning it off completely will use less energy than sleep or hibernate modes, depending on how much you use the computer, but you will need to allow more time for booting up.

At any rate, if you have a PC, run a C-cleaner before shutdown so viruses your firewall has missed (because it has missed some) can't install themselves on reboot. This will keep your computer from slowing down for the other obvious reason.

I shut it off because there are small electric motors in it that will wear out eventually. I guess it's OK to use the sleep mode because those motors turn off but it's a waste of electricity.