I leave my computer on 24/7 and just let it sleep as necessary.
I don't think that leaving it on will appreciably shorten the life of the components. This fan I have sitting in front of me has an estimated lifetime of 50,000 hours. That's 5 years of 24/7 operation in normal people time. Unsure what other components are rated at, but you might expect something similar.
However, you are going to use less energy if you shut down...though if you really want to save energy, completely unplug it too, as most modern electronics still draw a little power while "turned off".