There are both pros and cons when deciding whether or not to shut your computer down at night. Let's discuss the pros first. Say for example that your computer is on and the power goes out. There is the potential that your computer could be damaged. If there were programs running then you could also lose data. If your computer is off then you do not have to worry about this.
There are also some cons. Turning off your computer takes time. So you need to ask yourself if it is worth taking the time every night to shut it down.
Remember that if your computer is in hibernate mode then it is not using very much electricity at all but it is still using some. You will be saving some money.