It doesn't matter, you will hear many opposing opinions. Personally I prefer to keep my pc on all the time. You can certainly leave the modem and turn the PC off, but it is purely your choice.

Main reasons for me leaving it on all the time.

Access needed on an ad hoc basis,
Less wear and tear on hardware (not particularly relevant with todays hardware)
Cost of leaving on not exorbitant

"Man's mind once stretched by a new idea, never regains its original dimension."
- Oliver Wendell Holmes