as long as you have good antivirus and firewall there shouldn't be any problems leaving it on

I keep my modem on all the time.  It ensures connectivity to the line is maintained.  Also, with many newer and fast PC's, if you power up the PC and the modem at the same time, the PC will boot up before the modem is fully syncronized and operational and in those cases you will get an error message that you can't connect to the internet (modem). 

With the PC powered off, there is no danger to the PC from a hacker, virus, etc.

Thanks to both of you, I dont get any inbound intrusions in my ZA anymore since I have this router so its doing a good job, so basically what you are saying that the only time you are 100% safe is when computer is off.    Ronnie

Obviously turning the PC off is going to be "`100% safe".  But with a router and firewall software that is kept up to date, you are 99% safe (you can never be 100% unless it is powered off). 

 fireberd: Thanks for that.