That's up to you and your needs for the computer.It also depends on the operating system that you're using. (Unfortunately, you didn't give us that information.) There are a number of opinions on this subject..."when" and "How often" to turn off a computer...but here's my idea on the subject.
Unless you're going to be using the computer at night, turn it off. Let it rest. It uses power/money/resources and will wear out various moving parts sooner, at least as they relate to your ability to use the machine. Heat is not good for computers and the longer they're "hot", the quicker they'll have problems. If you're using a Win 9.x or ME computer, they will need to be restarted occasionally, (usually once per day) in order to recover resources. If you're using an NT based computer (NT, 2000, or XP), they have the ability to run for long periods of time without restarting, if needed.
Our work machines can be "servers", which run constantly, or desktop work-stations, which are turned on in the morning and off at the end of the day. With my personal computers I turn them on when I'm using them and turn them off when I'm not. I don't use the power management features for "Standby" etc. because I leave the machine on those days that I'm home. If I'm going to leave the house for 3 or 4 hours, or more, I turn the machine off. If not, I just leave it running.
In addition, if you're going to be leaving a computer on 24/7, make sure you monitor it frequently. Although not common, electrical fires, shorts, or those types of things are possible.
Hope this helps.