Roger is right that if you leave it on and have automatic update selected, you will get a lot of updates to begin with.
Turning computers on and off has been the subject of a lot of debate. There are proponents on both sides of the issue.
Personally, we have had a cable connection for a long time and I tend to leave my computer on for days at a time. The darn things take so long to boot up with firewalls and antivirus software, etc, etc that I don't have the patience to wait for it. I would leave it on permanently but I've noticed that my computer's performance begins to degrade after a few days if it is not allowed to go through it's shutdown routine. I used to run Ad-Aware and a spy finder program that cleaned out the temporary files and cookies then restart once a week after Norton Anti-Virus did it's weekly thing but recently switched to twice a week because of all the tracking cookies that one acquires these days.
More than you wanted to know.... Actually - it becomes your choice.