I actually joined these forums just to respond to this after seeing all the comments because I loved these answers so much.
Working in tech support, I've come to discover that the people who never reboot their devices or better yet - never shut off their devices - are always the ones to complain about the following:
Slowness
Freezing
Wifi issues
Battery life
Always. Then when you ask them the age old question "when's the last time you shut off the device or restarted it?" And they look at you like you have antlers growing from your forehead "no, why would I do that?"
The old wives tale of "using too much power to shut it down" or "wearing out the components by turning the computer on and off" is rubbish and makes no sense; as well as having no actual research to back the claim. If that was the case, you would never stop your washer and dryer, dishwasher - do you always keep your TV on?
I've shut off my original iPad every night since I got it launch day. Apple just ran a diagnostic on it last week because my mother bought it in to them (as she owns it now) and they told her the battery was at 90% capacity - the Genius was shocked for a 4 year old battery.
There's no harm in doing it - in fact you may see more benefits than you can imagine - on iOS devices, and other devices as well.